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PROCEEDINGS 

OF THE 

ROYAL SOCIETY OF EDINBURGH. 



PROCEEDINGS 



OF 

THE ROYAL SOCIETY 



EDINBURGH. 



VOL. XXXIV. 



NOVEMBER 1913 to JULY 1914. 



2 3 ( 8 '!^ 



EDINBURGH: 

PRINTED BY NEILL AND COMPANY, LIMITED. 



MDCCCCXIV, 



CONTENTS. 



PAGE 

Presentation of Bust of Lord Kelvin. (With Frontispiece ), ... 1 

1. Opening Address by the President, Professor James Geikie, LL.D., D.C.L., 

F.R.S., F.G.S., delivered at the First Ordinary Meeting for the Session, held 
on November 3, 1913, ........ 4 

2. Observations on the Auditory 0 gan in the Cetacea. By Principal Sir Wm. 

Turner, K.C.B., D.C.L., F.R.S. Issued separately December 31, 1913, . 10 

3. Note on a Siliceous Sponge of the Order Hexactinellida from South Shetland. 

By Principal Sir William Turner, K.C.B., D.C.L., F.R.S. Issued separately 
December 31, 1913, ........ 23 

4. Some Factorable Minors of a Compound Determinant. By Professor W. H. 

Metzler. Issued separately December 31, 1913, . . . .27 

5. The Theory of Bigradients from 1859 to 1880. By Thomas Muir, LL.D. 

Issued separately February 19, 1914, ...... 32 

6. The Kinetic Energy of Viscous Flow through a Circular Tube. By Professor 

A. H. Gibson, D.Sc., University College, Dundee. Issued separately 
February 19, 1914, ........ 60 

7. The Axial Inclination of Curves of Thermoelectric Force : a Case from the 

Thermoelectrics of Strained Wires. By John M‘Whan, M.A., Ph.D., 
Lecturer in Mathematics in the University of Glasgow. Communicated by 
Professor Andrew Gray, LL.D., F.R.S. Issued separately March 20, 1914, . 64 

8. The Path of a Ray of Light in a Rotating Homogeneous and Isotropic Solid. 

By E. M. Anderson, M.A., B.Sc. Communicated by The General Secretary. 

Issued separately March 20, 1914, . . . . . . 69 

9. Principia Atmospherica : a Study of the Circulation of the Atmosphere. An 

Address delivered at the request of the Council before the Royal Society of 
Edinburgh, on December 1, 1913. By W. N. Shaw, LL.D., Sc.D., F.R.S., 
Director of the Meteorological Office, Reader in Meteorology in the University 
of London. Issued separately March 23, 1914, . . . . 77 

10. Enzymatic Peptolysis in Germinating Seeds. By Dorothy Court, B.Sc., Carnegie 

Research Fellow. Communicated by Professor E. Westergaard. Issued 
separately March 26, 1914, . . . . . . .113 

11. A Study of the Curvatures of the Tasmanian Aboriginal Cranium. By L. W. G. 

Buchner, Victorian Government Research Scholar in the Anthropology 
Department of the University of Melbourne. Communicated by Professor 
R. J. A. Berry. (With Three Folding Tables.) Issued separately April 28, 

1914, 



128 



VI 



Contents. 



I’AGE 

12. The Place in Nature of the Tasmanian Aboriginal as deduced from a Study of 

his Calvaria. — Part II. His Relation to the Australian Aboriginal. By 
Richard J. A. Berry, M.D. Edin., Professor of Anatomy in the University of 
Melbourne ; and A. W. D. Robertson, M.D. Melb., Government Research 
Scholar in the Anatomy Department of the University of Melbourne. (With 
One Folding Table.) Issued separately April 29, 1914, . . . 144 

13. A Chemical Examination of the Organic Matter in Oil-Shales. By John B. 

Robertson, M.A., B.Sc., Carnegie Scholar. Communicated by Dr J. S. Flett, 

F.R.S. Issued separately July 15, 1914, . . . . . 190 

14. Notes on the Atmospheric Electrical Potential Gradient in the Industrial Dis- 

tricts around Leeds. By Dan. W. Steuart and Ingvar Jorgensen. Com- 
municated by James A. S. Watson, B.Sc. Issued separately July 14, 1914, . 202 

15. On the Hall and the Transverse Thermomagnetic Effects and their Temperature 

Coefficients. By F. Unwin, M.Sc., Assistant Lecturer in Physics, Heriot- 
Watt College, Edinburgh. Communicated by Professor F. G. Baily. Issued 
separately August 4, 1914, ....... 208 

16. Some Factorable Continuants. By W. H. Metzler, Ph.D. Issued separately 

September 3, 1914, . . . . . . . . 223 

17. The Analytical Study of the Mechanism of Writing. By James Drever, M.A., 

B.Sc. Communicated by Dr Alexander Morgan. Issued separately September 

3, 1914, . . . . . . . . .230 

18. Abnormal Echinoids in the Collection of the Royal Scottish Museum. By 

James Ritchie, M.A., D.Sc., Royal Scottish Museum ; and James A. Todd, 

M.A., B.Sc. Communicated by William Eagle Clarke. (With a Plate.) 

Issued separately September 4, 1914, ...... 241 

19. Description of a Projection-Model of the 600-Cell in Space of Four Dimensions. 

By D. M. Y. Sominerville, M.A., D.Sc., Lecturer in Mathematics, University 
of St Andrews. (With a Plate.) Issued separately September 29, 1914, . 253 

20. Changes of Electrical Resistance accompanying Longitudinal and Transverse 

Magnetizations in Iron and Steel. By Professor C. G. Knott, D.Sc. Issued 
separately December 14, 1914, ....... 259 

Obituary Notices — 

Dr A. C. L. G. Gunther, M.A., Ph.D., M.D., LL.D., F.R.S., etc., . . 269 

John Sturgeon Mackay, M.A., LL.D., ...... 278 

Professor John Gibson, ........ 285 

Appendix — 

Laws of the Society, . ...... 293 

The Keith, Makdougall-Brisbane, Neill, and Gunning Victoria Jubilee Prizes, . 298 

Awards of the Keith, Makdougall-Brisbane, Neill, and Gunning Victoria Jubilee 

Prizes, .......... 300 

Proceedings of the Statutory General Meeting, October 1913, 305 

Proceedings of the Ordinary Meetings, Session 1913-1914, . . . 306 

Proceedings of the Statutory General Meeting, October 1914, . . . 312 

Accounts of the Society, Session 1913-1914, , 313 



Contents. vii 

PAGE 

Appendix — continued. 

The Council of the Society at January 1915, ..... 319 

Alphabetical List of the Ordinary Fellows of the Society at January 1915, . 320 

List of Honorary Fellows of the Society at January 1915, . . . 337 

List of Ordinary Fellows of the Society elected during Session 1913-1914, . 339 

Honorary Fellows and Ordinary Fellows deceased and resigned during Session 

1913-1914 . . . . . ... . .339 

List of Library Exchanges, . ..... 340 

List of Periodicals purchased by the Society ..... 364 

Additions to Library during 1914, by Gift or Purchase .... 368 

Index, ........... 370 



PROCEEDINGS 

OF THE 



lns tifu f/ 




APR 18 1914 

JV at: 



ROYAL SOCIETY OF EDINBURGH. 



SESSION 1913-14. 



Part I.] VOL. XXXIV. [Pp. 1-112. 



CONTENTS. 

NO. PAGE 

Presentation of Bust of Lord Kelvin. (With Frontispiece), . 1 

I. Opening Address by the President, Professor James Geikie, 

LL.D., D C.L., F.R.S., F.G.S., delivered at the First Ordinary 
Meeting for the Session, held on November 3, 1913, . 4 

II. Observations on the Auditory Organ in the Cetacea. By 

Principal Sir Wm. Turner, K.C.B., D.C.L., F.R.S., . . 10 

{Issued separately December 31, 1913.) 

III. Note on a Siliceous Sponge of the Order Hexactinellida from 
South Shetland. By Principal Sir William Turner, K.C.B., 

D.C.L., F.R.S., . . ... . .23 

{Issued separately December 31, 1913.) 

IY. Some Factorable Minors of a Compound Determinant. By 

Professor W. H. Metzler, . . ; . .27 

{Issued separately December 31, 1913.) 

Y. The Theory of Bigradients from 1859 to 1880. By Thomas 

Muir, LL.D., 32 

{Issued separately February 19 1914.) 

YI. The Kinetic Energy of Yiscous Flow through a Circular Tube. 

By Professor A. H. Gibson, D.Sc., University College, Dundee, 60 

{Issued separately February 19, 1914.) 

EDINBURGH : 

Published by ROBERT GRANT & SON, 107 Princes Street, and 
WILLIAMS & NORGATE, 14 Henrietta Street, Covent Garden, London. 



MDCCCCXIY. 

Price Six Shillings and Sixpence. 



REGULATIONS REGARDING THE PUBLICATION OF PAPERS 
IN THE PROCEEDINGS AND TRANSACTIONS OF THE 
SOCIETY. 

The Council beg to direct the attention of authors of communications to 
the Society to the following Regulations, which have been drawn up in 
order to accelerate the publication of the Proceedings and Transactions, 
and to utilise as widely and as fairly as possible the funds which the 
Society devotes to the publication of Scientific and Literary Researches. 

1. Manuscript of Papers. — As soon as any paper has been passed 
for publication, either in its original or in any altered form, and has been 
made ready for publication by the author, it is sent to the printer. 

2. Method of Publication. — As soon as the final revise of a Trans- 
actions paper has been returned, or as soon as the sheet in which the last 
part of a Proceedings paper appears is ready for press, a certain number 
of separate copies or reprints, in covers bearing the title of the paper and 
the name of the author, are printed off and placed on sale. The date of 
such separate publication will be printed on each paper. 

3. Additions to a Paper after it has been finally handed in for 
publication, if accepted by the Council, will be treated and dated as 
separate communications, and may, or may not, be printed immediately 
after the original paper. 

4. Brief Abstracts of Transactions Papers will be published in 
the Proceedings, provided they are sent along with the original paper. 

5 Special Discussion of Papers accepted for Publication. — 
Where a paper has been accepted for publication, the Council may, with 
the consent of the author, select this paper for Special Discussion. In the 
case of such papers advanced proofs will be sent to the members of the 
Society desiring copies, and copies will be supplied to the author for dis- 
tribution. A paper selected for Special Discussion will be marked with an 
asterisk (*) and placed first on the Billet for the day of reading. Any 
following papers for that day may be adjourned or held as read if the 
discussion prevents their being read. 

6. Communications not submitted for Publication, such as 
Demonstrations of Experiments, Statement of Scientific Problems, etc., 
may be received by the Council, and may also be selected for Special 
Discussion. The Council does not undertake to publish any notice of such 
communications in the Proceedings or Transactions of the Society. 



[Continued on page iii of Cover . 



► * 











Proc. Roy. Soc. Edin. ] 



[Yol. XXXI Y. 




THE RIGHT HON. LORD KELYIN, G.C.Y.O., F.R.S., 
President of the Royal Society of Edinburgh, 1873-1878, 1886-1890, 
and 1895-1907. 



[. Frontispiece 




PROCEEDINGS 




OF THE 



ROYAL SOCIETY OF EDINBURGH. 



YOL. XXXIV. 



1913-14. 



Presentation of Bust of Lord Kelvin. 

The General Statutory Meeting of the Royal Society of Edinburgh was 
held in 24 George Street on Monday, 27th October 1913, at 4.30 p.m. 

Principal Sir William Turner, K.C.B., President, in the chair. 

Before the transaction of the usual business, the bust of Lord Kelvin 
(see frontispiece), which had been gifted to the Royal Society of Edinburgh 
by Lady Kelvin, was presented by Professor Crum Brown, acting for Lady 
Kelvin, and received by the President for the Society. 

Professor Crum Brown said : — 

“ Mr President, Fellows of the Royal Society of Edinburgh, 
Ladies and Gentlemen, — Lady Kelvin, knowing the great interest Lord 
Kelvin always took in the Royal Society of Edinburgh, and knowing also 
the high admiration and warm affection of the Fellows of the Society for 
their late President, has, with thoughtful kindness, expressed the wish to 
give this beautiful bust, by Mr Shannan, to remain in the rooms of the 
Society as a permanent memorial, and has asked me to present it in her 
name. I feel very highly honoured by Lady Kelvin’s request. I have had 
the great privilege of intimate acquaintance with Lord Kelvin since my 
boyhood, and it is impossible for me to tell how much I owe to him. 

“ I shall not attempt a review of Lord Kelvin’s work or character, but I 
may remind you of his supreme love of truth and of his intense interest in 
everything, however apparently trivial, connected with the constitution or 
with the working of the physical universe. These were the prime motives 
to his work, and he carried it out in the same spirit. Having formulated a 
problem, he followed the straightest road to its solution. Of course he 
encountered difficulties : these he did not evade, he surmounted them. To 

do so he had often to invent and construct special instruments of wholly 

VOL. xxxiv. 1 



2 Proceedings of the 'Royal Society of Edinburgh. [Sess. 

novel type. These were always marked by singular ingenuity, and designed 
so that they do the work for which they were made with the greatest 
possible accuracy. Lord Kelvin was a great mathematician. We all 
remember the “ green books,” always at hand, in which he worked out the 
mathematical analysis of the data obtained in his experiments, and of any- 
thing else he wished to subject to mathematical treatment. He was never 
at a loss to find the mathematical key. He made no show of abstruse 
formulae. In his mathematical as in his experimental work he took the 
most direct and the simplest way consistent with accuracy. Lord Kelvin 
was no intellectual miser. When, in the course of his scientific work, he 
came across something which could be so applied as to be of practical 
use, he developed this application, and thus became the inventor of 
truly scientific instruments, differing in character from those he made for 
purely scientific purposes only in this, that they are also used and very 
highly prized by those who are not necessarily scientific, who perhaps do 
not care about the dissipation of energy or vortex motion. These practical 
men come, by using Lord Kelvin’s inventions, to see that pure science is not 
vain ; they come to know something of the tree from its fruit. Lord Kelvin 
was quite free from selfishness or jealousy. He rejoiced in his own work 
and discoveries ; he rejoiced also in the discoveries of others. I recollect very 
well his enthusiasm over the work of Becquerel, of Crookes, of Dewar, of 
Graham Bell, and of many others. In the questions of first importance to 
man, where science gives no help, Lord Kelvin was a humble and devout 
disciple. In Lady Kelvin’s name I hand over to the Royal Society of 
Edinburgh, through you, Sir, as President, this beautiful work of art and 
striking likeness of Lord Kelvin, one of the greatest discoverers in pure 
science, a true benefactor of mankind, our honoured President and dear 
friend.” 

After the bust was unveiled, Sir William Turner received it in the name 
of the Society with the following words : — 

“ I feel sure that no more appropriate Fellow of the Society could have 
been chosen to act as spokesman on this occasion than our dear colleague 
and friend, Professor Crum Brown. He has given so admirable a summary 
of Lord Kelvin’s character and intellectual power as one of the great 
scientific men of the age that I need not attempt to follow him in that 
direction. But, speaking as the President of the Society, and speaking in 
regard to the man who immediately preceded me in the presidential chair, 
I think it might be useful and instructive to say a few words about Lord 
Kelvin as Fellow of the Royal Society of Edinburgh. I find that Lord 
Kelvin joined the Society in 1847. He remained a Fellow for sixty years. 



3 



1913-14.] Presentation of Bust of Lord Kelvin 

Two years after he joined the Society, he made his first communication, 
which was printed in our Transactions for the year 1849. It is interesting 
to note that this communication was on the subject of heat, and for ten 
years after that date he produced a series of most important memoirs 
on heat and other forms of activity, showing himself to be one of the 
most active-minded and original-minded men engaged in physical science. 
Our Transactions are a valuable record of all the early work which 
he gave to the world; and he looked upon the Society as the medium 
through which his ideas were to be submitted to the consideration of his 
fellow men of science. 

“ I can only refer to the numerous communications Kelvin made to the 
Society ; and it is interesting to note that there was a communication from 
him in our Proceedings for 1906, the year before he died. This was a 
great feature in Lord Kelvin’s intellectual career — he had an active mind 
to the end. The last communication published in our Proceedings was on 
the initiation of deep-sea waves. The sea and the deep sea exercised 
indeed an important influence over his practical career. As we all know, 
it was through Lord Kelvin’s investigations that the laying and the 
commercial working of the Atlantic cable were brought about, and his 
improved compass has been a boon to all seamen. In 1873 Kelvin was 
elected our President for the period of five years. In 1886 he was for a 
second time chosen for a similar period. He had served for four years of 
the second period when the Council of our Society received an informal 
intimation from the Council of the Royal Society of London that they wished 
Lord Kelvin to be their President. It was felt that it would be difficult 
to discharge the duties of this office if he remained President of the 
Edinburgh Royal Society. Accordingly it was suggested that we might 
be able to surrender Lord Kelvin to the Royal Society of London. This 
our Council agreed to do ; and in 1890 Lord Kelvin became their President. 
When in 1895 he retired from his Presidentship in London, he was for the 
third time appointed our President, and he continued in this office till his 
death in 1907. We can at once understand how Lady Kelvin should feel 
desirous that, so far as marble can perpetuate personality and expression, 
there should be such a perpetual memorial of her great husband in the 
building of the Society which he had adorned in the double capacity of 
Fellow and President. I ask Professor Crum Brown, as the mouthpiece of 
Lady Kelvin on this occasion, to be good enough to convey to her Ladyship 
our most devoted and hearty thanks for this admirable bust of her late 
husband, which will form one of the precious possessions of the Society.” 



4 



Proceedings of the Royal Society of Edinburgh. [Sess. 



I. — Opening Address by the President, Professor James Geikie, 

LL.D., D.C.L., F.R.S., F.G.S., delivered at the First Ordinary Meeting 
for the Session, held on November 3, 1913. 

Gentlemen, — For the high honour you have done me in electing me to the 
Presidency of this, the premier scientific Society of Scotland, I offer you 
my grateful thanks. I am proud indeed that you should have deemed me 
not unworthy to succeed the eminent men who have heretofore occupied 
this chair. My complacency, however, is tempered, if not subdued, by the 
consciousness of my own limitations. But if I cannot, like my predecessors, 
add lustre to the office I hold, I can at least endeavour to devote all my 
energies to the performance of its duties. 

It is matter of sincere congratulation that our Society continues to 
prosper, and to keep up its reputation by the number and value of its 
contributions to the stock of knowledge. During the past session no fewer 
than 46 papers were communicated. Of these 19 dealt with chemical and 
physical subjects; 19 were zoological; 3 botanical; 2 geological ; while 
pure mathematics, engineering, and anthropology were each represented 
by one paper. In addition to these papers, two addresses were delivered 
at the request of the Council — one being physiological and the other 
astronomical. 

During the session, I regret to say, our Society has sustained not a few 
losses — twenty-three of our fellow-members having died. Of this number, 
some will be long remembered by us not only for the distinction of their 
own careers, but for the active part they took in conducting the affairs of 
the Society. 

Ramsay Heatley Traquair, M.D., LL.D., F.R.S., F.G.S. . . . Dr 
Traquair became a Fellow of the Society in 1874, and served many years 
on the Council — his first term of office being from 1875 to 1878, and his last 
from 1904 to 1910, when he acted as Vice-President. He communicated 
many important papers to the Society, and was awarded the Makdougall- 
Brisbane and Neill Medals. Dr Traquair died on 24th November 1912, 
. . . [See Obituary Notice, Proceedings , vol. xxxiii. pp. 336-341.] 

John William Shepherd, Glasgow, was elected in 1897. He died on 
26th November 1912. 



5 



1913-14.] Opening Address by the President. 

Andrew Jamieson, M.Inst.C.E. . . . He was elected a Fellow of the 
Society in 1882, and died on 4th December 1912. . . . [See Obituary 
Notice, Proceedings , vol. xxxiii. pp. 334, 335.] 

Sir George Howard Darwin, K.C.B., M.A., LL.D., F.R.S., second son 
of the famous naturalist, was born in 1845, and died on 7th December 1912. 
After a brilliant career at Cambridge, he became barrister in 1874, but 
subsequently returned to Cambridge and devoted himself to mathematical 
science, and in 1883 was elected Plumian Professor of Astronomy and Experi- 
mental Philosophy. He is the author of many important and suggestive 
papers, a number of which appeared in the Proceedings and Philosophical 
Transactions of the Royal Society, of which Society he became a Fellow 
in 1879, and was the recipient of the Copley and Royal Medals. The great 
merits of his original researches have been recognised by many Universities 
at home and abroad, and by learned Academies and Institutions all the 
world over, who have enrolled his name among their hon. members. He 
was elected an Honorary Fellow of this Society in 1897. 

Lieut.-Col. Frederick Bailey obtained his commission in the Royal 
Engineers in 1859, and went to India in 1864, where he served in the 
Bhutan Expedition of 1864-5, for which he obtained a medal. In 1871 he 
was attached to the Indian forest service, in which department he remained 
for close on twenty years, having during that long period occupied several 
very important posts. So highly were his services appreciated by the 
Indian Government that he was eventually appointed Inspector-General 
of Forests. In 1890 temporary illness compelled him to return to this 
country. About this time the importance of Forestry as a branch of 
University education had been recognised by the institution of a Lecture- 
ship on the subject in the University of Edinburgh, and Lieut.-Col. Bailey 
was called upon to become first lecturer. He threw himself with charac- 
teristic zeal into his work, and soon gained the confidence of his students 
and the admiration of his colleagues. It is chiefly due to his indefatigable 
exertions that a degree in Forestry was eventually instituted by the 
University Court. Nor can it be doubted that it is to his energy and 
enthusiasm that the subject of Forestry now occupies so prominent a 
position not only in the University of Edinburgh but in Scotland generally. 
Lieut.-Col. Bailey also found additional outlets for his energies as an active 
member of the Royal Scottish Arboricultural Society, and as Secretary of the 
Royal Scottish Geographical Society. This latter post he occupied with 
conspicuous ability for many years, until the increasing work of his Lecture- 



6 



Proceedings of the Royal Society of Edinburgh. [Sess. 

ship compelled him in 1903 to resign. For four years longer he retained 
his position at college, when, to the regret of his colleagues, failing 
health obliged him to retire. Lieut.-Col. Bailey was elected a Fellow of 
the Society in 1894, and served one term on the Council (1896-99). His 
death took place on 21st December 1912. 

John M £ Arthur, F.C.S., Sussex. . . . He was elected to the Fellowship 
of the Society in 1888, and died on 19th December 1912. . . . [See Obituary 
Notice, Proceedings, vol. xxxiii. p. 333.] 

Robert M. Ferguson, Ph.D., LL.D., who died on 31st December 
1912, at the advanced age of 84, was elected a Fellow in 1868, and served 
three terms on the Council. He acted also as the representative of the 
Society on George Heriot’s Trust. . . . [See Obituary Notice, Proceedings, 
vol. xxxiii. pp. 342-345.] 

A. Beatson Bell, advocate, of Kilduncan, Kingsbarns, Fife, and a 
former Chairman of H.M. Prison Commissioners for Scotland, died on 
6th January 1913, in his 81st year. He was elected a Fellow in 1886, 
and served three terms on the Council. Mr Bell was all his life much 
interested in educational matters, having acted as a director of Edinburgh 
Academy, a governor of Donaldson’s Hospital, and a governor of the 
Trust for Education in the Highlands. He held various other important 
positions, such as director of the Royal Institution for the Home Relief 
of Incurables, and director of the Royal Sick Children’s Hospital. He 
was also a Fellow of the Royal Scottish Society of Arts, and served as 
President of that Society from 1897 to 1899. 

George Alexander Gibson, D.Sc., M.D., LL.D., F.R.C.P.E., was elected 
a Fellow in 1881, and served one term on the Council. He died on 18th 
January 1913, in his 59th year. I need not attempt to appraise Dr 
Gibson’s position as a medical man — we know that he was a brilliant 
member of his profession, respected and beloved by all who knew him. 
It is hardly too much to say that the premature death of this distinguished 
physician has been mourned by the whole community, and has been felt 
as a great loss to this Society. 

Sir William White, K.C.B., F.R.S., London, was elected a Fellow in 
1890. Sir William, who has been called “ the father of the modern British 
Navy,” had a most notable career. With no advantages of fortune or social 
position, he worked his way in the Naval service from the humble posi- 
tion of a shipwright apprentice to the important position of Director of 



7 



1913-14.] Opening Address by the President. 

Naval Construction. Under his superintendence some two hundred and 
fifty ships of various types were added to our Navy at a cost of about one 
hundred millions sterling, and for the work of construction of that great fleet 
Sir William was ultimately responsible. He died on 27th February 1913, 
in the 68th year of his age. 

J. J. Kirk Duncanson, M.D., studied medicine at Edinburgh and various 
medical schools on the Continent. He graduated M.D. at the University of 
Edinburgh in 1871, was elected to the Fellowship of our Society in 1890, 
and died on 12th March 1913. 

Walter Whitehead, F.R.C.S.E., was formerly Professor in Clinical 
Surgery in Victoria University, Manchester; past-President of the British 
Medical Association ; and author of many important works in surgery. He 
was elected a Fellow in 1881, and died on 19th August 1913. 

James Gordon MacGregor, D.Sc., LL.D , F.R.S., Professor of Natural 
Philosophy in the University of Edinburgh, passed away very suddenly on 
21st May 1913. He was elected to our Fellowship in 1880, and served one 
term on the Council. His genuine character had endeared him to a wide 
circle of friends, who could not but appreciate his kindly, frank manner and 
engaging simplicity ; while the whole-hearted zeal with which he devoted 
himself to his duties gained the admiration of his colleagues. Professor 
MacGregor was a sterling man, whose premature death was deeply 
regretted. 

William Colin Mackenzie, M.D., F.R.C.S., Melbourne, Australia, who 
was elected a Fellow of the Society in 1905, was Demonstrator in Anatomy 
in the University of Melbourne. 

John Penny, M.B., C.M., D.Sc., Cumberland, elected 1900, died 19th 
June 1913. He was a distinguished medical graduate of Edinburgh 
University, who afterwards specialised in the Department of Public Health, 
and obtained the degree of D.Sc. Although as a medical officer of health 
his time was largely occupied, he yet engaged actively in research, and con- 
tributed a number of important papers to various medical publications. 

William Gayton, M.D., M.R.C.P., M.R.C.S., etc., was elected to the 
Fellowship of the Society in 1900, and died in August 1913. He was 
Medical Superintendent of the N.W. Fever Hospital, and for thirteen years 
of Homerton Small -pox Hospital. Dr Gayton was the author of various 
papers on vaccination and small-pox. 



8 



Proceedings of the Royal Society of Edinburgh. [Sess. 



James M‘Cubbin, B.A., Kilsyth, was elected a Fellow of the Society in 
1899, and died on 2nd September 1913. He was latterly Rector of the 
Burgh Academy, Kilsyth. 

Hugh Marshall, D.Sc., F.R.S., Professor of Chemistry, Dundee Uni- 
versity College, was elected a Fellow in 1888, and died on 6th September 1913, 
at the early age of 46. He had a distinguished career at the University of 
Edinburgh, graduating as D.Sc., in his 21st year, a triumph which, so far 
as I know, is unique. He was for a number of years assistant to Professor 
Crum Brown, and Lecturer in the University on Mineralogy and Crystallo- 
graphy, until his appointment to the chair of Chemistry at Dundee in 1908. 
Although his time was much occupied in teaching, Professor Marshall yet 
found time to engage in original research, and published various valuable 
papers on chemical and crystallographical subjects. The quality of this 
research work was attested by the award of the Gunning “ Joseph Black ” 
Prize of the University, and of the Keith Prize and Medal of this Society, 
as also by his election to the Fellowship of the Royal Society of London. 

Alexander Macfarlane, M.A., D.Sc., LL.D., Ontario, Canada, was 
elected in 1878, and died in September 1913, aged 62. He greatly dis- 
tinguished himself as a student of mathematics in the University of 
Edinburgh, where he graduated as D.Sc. — his thesis, “ On Electric Sparks 
in Air,” appearing subsequently in the Transactions of this Society. For 
some time he acted as assistant to the late Professor Chrystal, and in 1885 
was appointed Professor of Physics in Texas University. He latterly 
devoted much attention to the study and development of vector algebras, 
his latest communication on the subject having been read before the 
Congress of Mathematicians which met at Cambridge in 1912. 

Sir Walter Noel Hartley, D.Sc., F.R.S., was elected in 1877, and died 
on 11th September 1913. He was Hon. Fellow of King’s College, London, 
and for some time Professor of Chemistry in the Royal College of Science 
for Ireland. He was author of works on air and its relations to life, and on 
water, air, and disinfectants, and communicated a number of papers to the 
Royal Society of London, the Fellowship of which he attained in 1884. He 
contributed also to the Journal of the Iron and Steel Institute, the Trans- 
actions of the Chemical Society, and to the publications of various other 
scientific institutions. Amongst the honours conferred upon him in re- 
cognition of his work he was awarded the Longstaff Medal of the Chemical 
Society for researches in spectro-chemistry. 



9 



1913-14.] Opening Address by the President. 

John Macmillan, M.A., D.Sc., M.B., C.M., etc., Edinburgh, was elected 
in 1876, and died on 7th October 1913. He was a brilliant student, first at 
St Andrews, where he graduated as M.A., and afterwards at the Uni- 
versity of Edinburgh, where he obtained the degree of B.Sc. Later on he 
entered upon the study of medicine at the same university, and graduated 
M.B., C.M., subsequently passing as B.Sc. in Public Health, and finally 
obtaining the doctorate of science. With such an academic career Dr 
Macmillan could hardly fail to make his mark in his profession, and by his 
medical brethren he was held in the highest esteem. As Lecturer in 
Medical Jurisprudence in the Extra-mural School of Medicine, Edinburgh, 
he was much appreciated by his pupils ; while as a practitioner he endeared 
himself to his patients by his unfailing kindness and sj^mpathy. 

Sir John Batty Tuke, M.D., D.Sc., LL.D., was elected in 1874, and 
served three terms on the Council; he died on 13th October 1913. 
Born in 1835, in Yorkshire, he came early to Edinburgh, and graduated in 
medicine in 1856. Shortly afterwards he went to New Zealand, where he 
was attached to the colonial forces as surgeon, becoming senior medical 
officer on the outbreak of the Maori War in 1860. On his return to this 
country he devoted himself especially to the treatment of mental diseases, 
and soon attained eminence in his profession. He occupied many im- 
portant positions as a medical man, and was twice elected to represent 
the Universities of St Andrews and Edinburgh in Parliament. During 
his term of office he naturally took great interest in all educational matters, 
and for these services, as well as for his eminence as a physician, he 
obtained honorary degrees from Trinity College, Dublin, and the University 
of Edinburgh. As member of Parliament for the Universities of Edinburgh 
and St Andrews he was of great service in pressing the claims of the 
Society upon the Government during the negotiations in regard to the 
removal of the Society from the Royal Institution to its present premises 
in George Street. 

William Donaldson, M.A., was elected in 1896, and died on 16th 
October 1913. For over thirty years he was headmaster and controller of 
Viewpark School — a private educational institute in this city. He was 
devoted to his profession, and held in high esteem by all who knew him — 
and by none more so than his pupils. 



10 



Proceedings of the Royal Society of Edinburgh. [Sess. 



II. — Observations on the Auditory Organ in the Cetacea. 

By Principal Sir Wm. Turner, K.C.B., D.C.L., F.R.S. 

(Read December 1, 1913. MS. received December 2, 1913.) 

Early in September of this year I received from the Falkland Islands 
a box, dispatched by Mr G. Millen Coughtrey, a former student of the 
University, now an employe in the New Zealand Whaling Company. It 
contained a number of specimens which illustrated the anatomy of the 
auditory apparatus in the Cetacea. The whales were caught in the South 
Atlantic, mostly at South Shetland, though some were from Graham’s Land, 
at which place he had been whaling last season. 

External Auditory Meatus and Earwax. 

The Cetacea do not possess an auricle or pinna of the ear. A small 
external opening capable of admitting a probe may be seen, when carefully 
looked for, at the side of the head, behind the outer angle of the eye. It 
is the orifice of the external auditory meatus, which penetrates the cutis 
and the thickness of the blubber to reach the tympano-petrous bone in 
which the essential parts of the organ of hearing are situated. The length 
of the meatus varies in different species. The lumen of the meatus may 
easily be overlooked, but it widens in its course, especially as it approaches 
the tympanic bone. It is usually destroyed in removing the blubber,* and 
has not received much attention in cetological literature. 

The presence in it of a ceruminous secretion, the earwax, has, however, 
been occasionally noted. Thomas Buchanan, surgeon in Hull nearly a 
century ago,f described and figured in 1828 dissections of the meatus and 
tympanum in the Greenland whale, Balcena mysticetus. He saw in the 
meatus an unctuous cerumen of a greyish-blue colour, “but in no great 
quantity.” He thought that the collapsed state of the orifice, the great 
length of the meatus, its winding course, a valve-like obstruction about its 
middle, and the unctuous secretion tended to prevent the passage of sea 
water down the auditory canal, in which none was present in the specimens 

* Robert Gray, “ Auricular Opening and External Auditory Meatus in Balcena 
mysticetus Journal Anat. and Phys ., vol. xxiii., 1889. 

t Physiological Illustrations of the Organ of Hearing , London, 1828. Hull at that time 
was the great shipping port of the whaling industry. 



11 



1913-14.] The Auditory Organ in the Cetacea. 

he dissected. Carte and Macalister described * the meatus in Balcenop- 
tera rostrata as lined by a pseudo-mucous membrane of modified cuticle, 
arranged in three longitudinal folds, and filled with a dark, greyish sebaceous 
substance produced in ceruminous glands, the openings of which were 
visible on the mucous membrane. The most recent account of the meatus 
and its contents has been, given by D. G. Lillie, j* He described in Baloe- 
noptera musculus the opening of the meatus, its course to the tympanum, 
where the lumen widened to 1^ inch diameter, and its relation to the mem- 
brana tympani. The meatus contained a solid plug of wax, the base or 
deep end of which was cup-like and moulded on the convex sac-like surface 
of the membrana tympani, which projected into the deep end of the 
meatus. The cup was about 1 inch deep and 1J inch in breadth. The 
plug of wax was about 5 inches long, and its outer part formed a thin 
flattened rod which lay in the inner half only of the meatus. Lillie stated 




Fig. 1. — Plug of earwax from meatus o LMegaptera longimana, slightly reduced in size. 



that the meatus appeared to be full of water, in which the wax and the 
tympanic sac were immersed. 

Mr Coughtrey’s collection contained several good specimens of plugs 
of dark, yellowish-brown earwax. 

Megaptera longimana . — A plug from each auditory meatus of a hump- 
backed whale, captured January 1913, was sent. One was complete, the 
other was not so perfect: they were 150 and 159 mm. (6 and inches) 
long respectively. The tympanic end, 22 mm. (about J inch) broad and 
10 mm. thick, was hollowed into a cup 22 mm. deep, which without doubt 
had been in close apposition with the convex sac-like tympanic membrane 
that had occupied the deep expanded part of the meatus (fig. 1). The plug 
gradually diminished in diameter, and at the opposite end it was flattened, 
only 12 mm. broad and 1 mm. thick. The surfaces of the plug were marked 
with shallow ridges and furrows which extended in its long diameter. 

A much smaller plug, 112 mm. long, was included in the collection. 
The tympanic end, not cup-like, had apparently been broken, its transverse 
diameter was 12 mm., and it rapidly narrowed to a point at the opposite 



* Trans. Roy. Soc. London , 1867. 

t Proc. Zool. Soc. London , p. 769, 1910, with figures and plate. 



12 



Proceedings of the Royal Society of Edinburgh. [Sess. 

end. The specimen was not labelled, but had probably been from the 
meatus of another Megaptera. 

Balcenoptera sibbaldi . — A single plug of earwax from one meatus of a 
Blue Whale, captured in South Shetland in 1912, was sent. It had been 
injured at the tympanic end, and only a portion of the cup-like cavity had 
been preserved. The plug was 50 cm. (nearly 20 inches) long, 26 mm. 
(1 inch) broad, and 12 mm. thick at its deep end. It gradually diminished 
in breadth and thickness, so that the opposite outer end, though 20 mm. 
(| inch) broad, was only 3 mm. thick, and possessed a flattened, ribbon-like 
aspect (fig 2, A). The surfaces of the plug were fluted longitudinally, and 




Fig. 2. — Earwax from meatus of Balcenoptera sibbaldi , natural size. A, outer fourth of plug with 
thin flattened end to the right ; B, tympanic end with cup -like depression. 



had doubtless been adapted to ridges and furrows on the surface of the lining 
membrane of the meatus. Cough tre} T had noted that the plug gave a very 
good impression of the canal in which it was situated. The tympanic end 
of a second plug, 80 mm. long, 34 mm. in greatest breadth, and 15 mm. 
thick, had been preserved. The cup-like cavity was nearly complete and 
was 15 mm. in depth (fig. 2, B). 

The length of the auditory meatus in the Cetacea bears a proportion to 
the thickness of the blubber on the side of the head. If the wax plug 
were in every case of equal length with the meatus, it would be a gauge to 
the thickness of the blubber, but in the specimen dissected by Lillie the 
plug was not equal in length to the meatus. I am not acquainted with 
any exact measurement of the thickness of the blubber on the side of the 
head in Megaptera. Sir John Struthers in his account of the Tay 



13 



1913-14.] The Auditory Organ in the Cetacea. 

Megaptera* gave 4 inches in the fore part of the carcase and 3 inches 
further back as the thickness of the blubber, but the length of the wax 
club in the South Shetland Megaptera indicated a greater thickness on 
the side of its head. In the Longniddry B. sibbaldi which I dissected in 
1869-70 f the blubber on the top of the beak and cranium was 8 to 15 
inches thick, whilst in front of the dorsal fin it was 12 to 16 inches, and 
behind that fin 14 to 21 inches. 

Tympano-petrous Bones. 

The collection contained the following specimens : — 

Megaptera longimana. — (a) Right and left tympano-petrous bones of the 
Humpbacked Whale, from a specimen captured in 1913 near Bryde Island, 
Graham’s Land; the tympanies were 109 and 113 mm. (4J and 4J inches) 
respectively in length. ( b ) Left tympano-petrous tympanic, 108 mm. long, 
(c) Right and left tympanies, 106 mm. long, (d) Right tympanic, 107 
mm. long. 

Balcenoptera sibbaldi. — (a) Three pairs of tympano-petrous bones of 
the Blue Whale from South Shetland, captured 1912, and (b) a single left 
tympanic. The tympanies as a rule varied in length from 121 to 129 mm., 
but one pair measured exceptionally 146 and 148 mm. (about 5f inches). 

Balcenoptera musculus . — A pair of tympano-petrous bones from a 
whale captured at Admiralty Bay, South Shetland, in November 1912, is 
labelled B.W., i.e. Blue Whale. The examination of these specimens 
satisfied me that the tympanic differed from that bone in B. sibbaldi in 
several particulars, as follows : It possessed a deep groove on the outer 
surface parallel and close to the posterior border, which gave to that border 
a more definite character than was the case in B. sibbaldi. On the other 
hand, it did not possess the long broad groove parallel to and bounding 
the outer side of the lower border, which gave rise in sibbaldi to a very 
prominent keel; the Eustachian end of the tympanic cleft was also less 
scooped out than in sibbaldi. The tympanic was 125 mm. long, 89 high, 
and 77 in greatest breadth. In one of the pair the opisthotic process of 
the petrous was entire, 435 mm. long by 135 mm. in greatest breadth, 
almost identical in its dimensions with those of a large B. sibbaldi. 

Differing from Sibbald’s Whale in several particulars, the tympanies 
more closely corresponded in their characters with B. musculus, so that I 
am disposed to regard this pair of specimens as from that species. 

* Anatomy of the Humpbacked Whale, Edinburgh, 1889. 

t Account of the great Finner Whale, stranded at Longniddry, Trans. Boy. Soc. 
Edin. } vol. xxvi., 1870. 



14 



Proceedings of the .Royal Society of Edinburgh. [Sess. 

This series of tympanies are of importance in showing that the 
Balsenopteridse, Megaptera longimana, Balcenoptera sibbaldi, and B. 
musculus, which frequent the North Atlantic and are; captured in Scottish 
waters, are also denizens of the South Atlantic. The University Museum 
also contains a pair of tympanic bones from Balcenoptera borealis, 
Rudolphi’s whale, the Sye Whale, from the South Atlantic,* captured in 
1911, which is also a Scottish species. 

Many naturalists have described with more or less detail the tympano- 
petrous bones in the whalebone and toothed whales. I have also figured 
in my descriptive Catalogue f the characters of the tympanies in a large 
number of species. The additions to the collection through the recent gift 
of Mr Coughtrey have enabled me to study more completely the relations 
of the tympanic and petrous bones to each other, to the chain of tympanic 
ossicles, and the approximate arrangement of the membrana tympani and 
the external auditory meatus. Carte and Macalister had previously given a 
careful description of the tympano-petrous in Balcenoptera rostrata, and 
Struthers had recorded their characters in Megaptera longimana, but the 
dissections of D. G. Lillie of the region in Balcenoptera musculus are much 
more complete, as he had the advantage of studying the bones along with 
the associated soft parts. The University collection contains specimens of 
these bones in both the whalebone and toothed whales ; they corresponded 
with each other in general characters, though with modifications in detail, 
which expressed specific and generic differences. In no specimen, however, 
had the external meatus, the tympanic membrane, and the Eustachian tube 
been preserved. 

The following description is based on the characters of the tympano- 
petrous bones in Balcenoptera sibbaldi, \ though with specific modifications it 
applies generally to the baleen whales. The tympanic bone was keeled on 
its inferior surface. Its outer surface was convex and marked by an 
oblique, strong, relatively wide groove-like depression which divided it into 
an anterior and a posterior part, the latter of which was the larger. The 
upper border of this surface was sinuous and was connected by a broad 
posterior pedicle to the under-border of the long, flattened, winglike opis- 
thotic process of the petrous. The anterior surface of the posterior pedicle 
was hollowed, smooth, directed towards the tympanic cavity and the meatus, 

* Catalogue, p. 58 ( G . Bpt., 5). I described a Scottish specimen in Journ. Anat. and 
Phys ., April, 1882. 

+ The Marine Mammals in the Anatomical Museum of the University of Edinburgh , 
London, 1912 ; also “ The Right Whale of the North Atlantic ( Balcena biscayensis )” in Trans. 
Boy. Soc. Edin ., vol. xlviii. part 4, 1913. 

I The University Museum now contains eighteen tympanic bones of Sibbald’s Whale. 



15 



1913-14.] The Auditory Organ in the Cetacea. 

and had evidently been invested by the tympanic membrane (fig. 3, Au), 
where it formed the cul-de-sac which projected into the auditory meatus ; 




Fig. 3. — Outer aspect of left tympano-petrous bones of Balcenoptera sibbaldi , natural size. A, 
anterior end, P, posterior end of tympanic ; Au, indicates the region adjoining the external 
auditory meatus covered by the tympanic membrane and the place of projection into meatus of 
tympanic membrane ; l , lip-like process of sinuous border with which malleus is fused ; M, 
head of malleus ; S, head of stapes in funnel-like depression on inner wall of tympanum ; L, 
labyrinthine part of petrous ; Pr, pre-otic, and Op, opisthotic parts of petrous cut across ; Ap, 
anterior, and Pp, posterior tympano-petrous peduncles. The incus is not figured, as it would 
have obscured the stapes. 



the smooth surface was bounded by a rough area, to which had doubtless 
been attached the deep end of the wall of the meatus. The sinuous border 



16 



Proceedings of the Royal Society of Edinburgh. [Sess. 

in front of the posterior pedicle was at first concave, then somewhat elevated, 
and was succeeded by a narrow, deep groove, which formed the posterior 
boundary of a strong curved process. I have elsewhere * named this process 
lip-like or mallear, for the malleus was fused with it ; it ascended towards 
but did not touch the under surface of the labyrinthine part of the petrous, 
and ended in a free rounded edge (fig. 3, l). At its front was the wide 
groove-like depression which separated the posterior from the anterior part 
of the outer surface of the tympanic. The upper border of this part of the 
surface was connected by a broad anterior pedicle *j* to the pre-otic division 
of the petrous. The labyrinthine or proper periotic division of the petrous 
was relatively small ; it lay between and gave origin to the pre-otic and 
opisthotic divisions of the bone, and it formed the roof and inner wall of 
the tympanic cavity (fig. 3, L). 

The gap between the anterior and posterior pedicles, the sinuous border, 
and the edge of the labyrinthine roof had without doubt been associated 
with the membrana tympani, and through the large part of the gap 
behind the lip-like process the sac-like prolongation of this membrane had 
projected into the lumen of the meatus, the wall of which had been attached 
to the margin of the gap. 

Buchanan, in his Illustrations (op. cit.), figured dissections of the dilated 
tympanic end of the meatus in Balcena mysticetus, and showed the sac -like 
surface of the tympanic membrane, which formed a convex projection into 
its lumen and was enclosed by its wall. He stated the sac to be divided 
internally into a major and a minor concavity by a valve-like membranous 
process from the wall, to the whole length of which the slender process of 
the malleus was attached, whilst the handle was connected with the outer 
edge of the osseous tympanum. Buchanan adopted the view of Sir Everard 
Home, that the membrana tympani had a muscular layer, to which he 
added a reticulated nervous plexus situated subjacent to the cuticle. 
KnoxJ saw in Balcenoptera rostrata a bag-like projection of the membrana 
tympani projecting into the auditory meatus; he stated that in a foetal 
Balcena mysticetus the membrane, though thick, is not muscular. The 
presence of muscular and nerve fibres in the membrane is not now accepted. 
Lillie, in his excellent description and figure of the membrana tympani in 
B. musculus, showed that it formed a sac, not unlike the finger of a glove, 
about 3 inches long and § inch in diameter, which projected into the dilated 

* Marine Mammals , op. cit. pp. 20, 74. 

t The anterior and posterior pedicles in Balcenoptera rostrata were thin plates of bone 
and were very easily fractured. 

tj; Catalogue of Anatomical Preparations of the JVhale, Edinburgh, 1838. 



17 



1913-14.] The Auditory Organ in the Cetacea. 

lumen of the auditory meatus, where its somewhat rounded end fitted into 
the cup-like base of the plug of wax. By its opposite end it was con- 
tinuous with the membranous lining of the tympanic cavity. A ligament 
about 1 inch long and 5 mm. broad sprang from the upper part of the 
sac, passed towards the tympanic cavity under the malleo-incal joint, and 
became attached to the manubrium of the malleus. The tympanic sac and 
the ligament were together about 4 inches long.* 

The Tympanic Ossicles are frequently missing in museum specimens, 
and I have carefully looked for them in the bullse of the whales in the 




Fig. 4. — Chain of left tympanic ossicles, tympanic cavity and cleft of Balcenoptera sibbaldi, natural 
size seen from above. A, anterior end of tympanic ; E, Eustachian end of cleft ; Ap, anterior 
tympano-petrous peduncle cut across ; l , lip-like process of sinuous border ; M, malleus with 
two processes fused with anterior border of lip ; I, incus ; S, stapes : their several articula- 
tions are represented. 

University collection. The incus, owing to the diarthrodial joints between 
it and the malleus and stapes being apt to give way, is seldom present, even 
when the malleus and stapes with their firmer attachments have been 
preserved. 

The Ossicles in B. sibbaldi will now be described. The upper end of the 
Malleus consisted of a rounded head with a groove separating it from the 
part of the bone which had on its inner aspect two articular surfaces for 
the incus set at an angle to each other. The diameter of the conjoined head 
and articular part was 16 mm. From the lower part of the head, a process 
descended, 18 mm. long, which was fused in its entire length with the 
anterior border of the lip-like process of the sinuous border of the tym- 
panic (fig. 4). A second descending process, parallel and close to the 

* I have figured in Marine Mammals a similar sac in Hyperoodon. 

VOL. XXXIV. 



2 



18 



Proceedings of the Royal Society of Edinburgh. [Sess. 

preceding, was similarly attached to the lip. These processes were brittle, 
and if the tympanic was roughly handled they easily broke and the malleus 
became detached and lost. The Incus had a body, 8 mm. in diameter, on 
which were two concave articulations for the malleus. A short, sharp 
process projected from the posterior surface and nearly reached the roof of 
the tympanic cavity. From the inner aspect sprang a longer curved process 
which, together with the body, measured 14 mm. ; at its free end was an 
oval facet for the stapes. The Stapes had a corresponding facet on its head, 
from which a pair of short relatively thick legs arose, to end in the plate- 
like foot of the stirrup. A very thin layer of bone passed between the legs 
and was pierced by a minute foramen. The stapes, 11 mm. long, occupied 
a funnel-shaped depression in the inner or petrosal wall of the tympanum, 
and its oval foot, 8 mm. in diameter, was attached to the fenestra ovalis 
of the cochlea (fig. 4). 

As the fusion of the malleus with the tympanic gave to the Cetacea 
an exceptional character as compared with other mammals, I may state 
the species in which I have noted this arrangement. In the whalebone 
whales I saw it in Balcena mysticetus and biscayensis, in Balcenoptera 
musculus, sibbaldi, borealis, rostrata, and in Megaptera longimana. In 
the toothed whales I saw it in Hyperoodon, Phocsena, Globicephalus, 
Grampus, Delphinus, Tursiops, and apparently in Monodon. In several 
other species in the University Museum the malleus was not in place and 
had not been preserved. It should be stated that previous observers have 
noted the fusion of the malleus with the tympanic in certain species. Knox 
saw it * in Balcenoptera sibbaldi and rostrata ; Carte and Macalister spoke 
of it in B. rostrata as a process of the tympanic bone, from the margin of 
whose centre it projected; Dwight described it in B. musculus as co-ossified 
with the tympanic by a processus longus, which had a deep groove anteriorly ; 
Lillie in B. musculus as fused to the inner edge of the lip of the tympanic. 

Different views have been expressed regarding the morphology of the 
processes of the malleus. By some, the process fused with the tympanic 
lip has been regarded as the manubrium or handle of the bone. Possibly 
the two parallel processes which I have figured in B. sibbaldi were only a 
twin-like arrangement of this process. Others, again, have considered the 
fused process to be the long slender (gracilis) process of the human anatomist. 
Buchanan, whilst recognising the handle as always attached to the outer 

* Knox, Catalogue , pp. 14, 21, who named the species Balcena maximus borealis and 
minimus ; Carte and Macalister, op. cit. ; Dwight in Memoirs of Boston Society of Nat. Hist., 
vol. ii. ; Lillie, Proc. Zool. Soc. London , 1910 ; Turner in Marine Mammals and in Memoir 
on Balcena biscayensis , Trans. Roy. Soc. Edin ., vol. xlviii., 1913. 



19 



1913-14.] The Auditory Organ in the Cetacea. 

-edge of the osseous tympanum, described in B. mysticetus the valvular 
fold of the tympanic membrane as attached to the whole length of the 
gracilis, or slender process. Lillie, again, considered that the only attach- 
ment of the membrane to the malleus in B. musculus was through the 
connection of the ligament to a short process, which he regarded as the 
manubrium, whilst the fused process was the processus gracilis. The de- 
velopment of these processes requires to be studied before their morphology 
can be precisely determined. 

The inner surface of the tympanic bone was separated from the outer by 
the tympanic cavity, the upper internal border of the former surface was thick, 
rounded, and striated, where it turned over into the cavity (fig. 4). This 
border was distant from the sinuous upper border of the outer surface by 
the width of the tympanic cleft, which extended forwards from the posterior 
pedicle to the anterior or Eustachian notch of the cleft. In the whalebone 
whales the cleft was approximately horizontal, though in the genus Bahama 
it had a deep notch at its anterior end.* In the toothed whales the cleft 
inclined downwards at this end and opened by a mouth immediately above 
the anterior end of the inferior surface. The Eustachian tube had not been 
preserved in my specimens. Mr Lillie has been more fortunate, and he has 
described in B. musculus a sac-like prolongation of the tympanic membrane 
through the Eustachian notch into the pterygoid fossa, from which the 
Eustachian tube proper arose as a relatively narrow canal, about one 
foot long, which extended forwards to open into the naso-pharyngeal 
chamber. 

Observations have been made in several toothed whales on the arrange- 
ment of the membrana tympani and its prolongation forwards into the 
sinuses in the cranio-facial bones. Buchanan described and figured the 
membrane in the Narwhal (Monodon) as nearly circular, concave towards 
the meatus, convex towards the tympanic cavity ; the manubrium of the 
malleus was, he said, attached to it. In the University Museum is the 
tympanic of a well -grown foetal Narwhal about 5 feet 5 inches long.j- 
The lip-like process of the sinuous border was prominent, and the gap 
between it and the posterior peduncle was occupied by the dried tympanic 
membrane, which did not bulge outwards towards the meatus. The malleus 
incus and stapes were present. The malleus had been attached to the lip- 
like process, but owing to the fragility of the bone it had broken away. 
The auditory arrangements in the Porpoise ( Phoccena communis) were 

* See the figures in my Memoir on the North Atlantic Balcena biscayensis , Travs. Roy. 
,Soc. Edin ., 1913. 

t Proc. Roy. Soc. Edin., vol. ix. p. 10?, 1876. 



20 



Proceedings of the Royal Society of Edinburgh. [Sess. 

figured by Monro secundus * who described a concave tympanic membrane 
at the bottom of the meatus ; a communication between the cavity of the 
tympanum and other cavities analogous to the human frontal, sphenoidal 
and maxillary sinuses ; an Eustachian tube which connected the tympanic 
cavity with the nasal chamber. The prolongation of the tympanic 
membrane into the air sinuses in these bones of the skull, as well as into 
the palate bone, has been described by Rappj* in the porpoise, and by 
Claudius l in Delphinus delphis, together with the relations of the ossicles 
to the tympanic membrane and the communication of the Eustachian tube 
with the cavity. 

The Petrous in the large whales is a heavy massive bone interlocked 
with the base of the skull, consisting of three definite divisions, a central 
labyrinthine part which contained the cochlea, vestibule, and semicircular 
canals, in which the auditory nerve was distributed ; a short anterior pre- 
otic process and a long posterior opisthotic process, as an example of 
which Balcenoptera sibbaldi may be described (rig. 3). The Labyrin- 
thine division had a rough upper surface in relation to the basis cranii ; a 
smooth under surface characterised by a large bluntly conical projection, 
which was directed outwards towards the tympanic, but separated from it 
by the cleft in the tympanic bulla. This surface also formed the roof and 
inner wall of the tympanic cavity ; in it was a funnel-like depression in 
which the stapes was situated and was attached by its foot to the fenestra 
ovalis of the cochlea. The inner aspect of the petrous was prolonged and 
perforated by the large canals for the passage to the labyrinth of the 
divisions of the auditory nerve, and by smaller foramina and canals. 

The Pre-otic was an irregular conical mass which projected forwards to 
end in a more or less pointed process, it was continuous with the labyrinthine 
division, and was connected with the tympanic by the anterior pedicle ; it 
occupied a depression in the squamous temporal above the pterygoid fossa. 
The Opisthotic, so-called mastoid, was a long flattened wing-like plate 
continuous with the labyrinthine division, and connected with the tympanic 
by the posterior pedicle. In one of my specimens of B. sibbaldi it was 
17 inches (432 mm.) long, and in another 5J inches (134 mm.) broad. It 
was locked into a groove between the squamous-temporal and the ex- 
occipital. In a Megaptera the greatest length was 235 mm., and the 
greatest breadth 100 mm. ; in B. musculus, 200 by 70 mm. ; in B. rostrata , 
70 by 35 mm. 

* “On Fishes,” p. 45, Edinburgh, 1785. 

t Die Gehorwerkzeuge der Cetaceen, Tubingen, 1836. Die Cetaceen, Stuttgart, 1837. 

J Physiologische Bemerkungen iiber das Gehororgan der Cetaceen , Kiel, 1858. 



21 



1913-14.] The Auditory Organ in the Cetacea. 

The auditory apparatus in the Cetacea has been modified in adaptation 
to the aquatic life of an air-breathing mammal, which can respire only 
during the relatively short period when the nasal opening or blowhole 
is above the surface of the water. There can be no doubt that the tym- 
panic cavity contains air, which it obtains during inspiration through the 
communication of its Eustachian tube with the naso-pharyngeal chamber. 
The immersion of the side of the head in the water renders unnecessary 
the development of an external auricle, capable of being turned in different 
directions to receive aerial sound waves, and the question naturally 
arises, how can sound waves be conveyed so as to impress the nerve 
apparatus in the whale’s labyrinth ? 

On this matter different opinions have been expressed. Buchanan 
considered * that the Eustachian tube and not the external meatus 
■“ conducted the pulsations of sound into the tympanum,” causing 
vibratory movements of its membrane and corresponding action in the 
chain of ossicles; whilst the meatus, through the width of its tympanic 
end, facilitated the vibratory movements of the sac-like prolongation of 
the membrane into it. This view has not, however, been accepted. 

Others have regarded the vibrations as excited by the aerial sound 
waves propagated down the external meatus, which directly impressed the 
membrane and were then conveyed by the chain of ossicles to the fenestra 
ovalis and labyrinth. As against this view it should be kept in mind that 
in the Cetacea the period is short and infrequent during which the external 
aperture is exposed to the air ; waves of sound could be transmitted only 
interm ittingly and not to much purpose. Sufficient evidence now exists 
that in the whalebone whales the meatus is blocked with a large 
plug of wax ; the lumen, therefore, cannot be occupied with air to permit 
the transmission through this medium of sound weaves. On the other 
hand, the wax-plug is a solid body closely moulded in these whales on the 
;sac-like membrane of the tympanum. As such it would doubtless transmit, 
as the cranial bones themselves can do, sound waves generated in the sur- 
rounding water, which would produce vibratory movements of the tympanic 
membrane and the chain of ossicles. In the baleen whales sufficient 
pressure exists in the air of the tympanum to produce the convex pouch- 
like projection of the membrane into the auditory meatus. 

Some years ago Claudius wrote an interesting memoir on this subject, f 
and argued that in the Cetacea the sound waves were not directly 
transmitted by the Eustachian tube, the meatus auditorius, or through 

* Op. cit. 

t Ueber das Gehororgan der Cetaceen, Kiel, 1858. 



22 



Proceedings of the Royal Society of Edinburgh. [Sess. 

the bones of the head to the nerves in the labyrinth ; but that the waves, 
detached themselves from the bones and thus impressed the air contained in 
the tympanic cavity and in the sac-like projection of its membrane in the- 
baleen whales, and its prolongations into the accessory sinuses in the 
dolphins. The waves might then act in two ways, either through the 
fenestra ovalis and fenestra rotunda, by impressing the lymph in the 
divisions of the labyrinth and through it the end organs of the auditory 
nerve, or by setting in movement the chain of ossicles which have as 
their fixed point of attachment the malleo-tympanic interossification. 

Claudius, therefore, thought that the sound waves reached the head of 
a Cetacean through the water in which it lived ; that they were trans- 
mitted by the bones of the head to the air in the tympanic cavity, and 
that the waves generated in it directly caused vibrations through the 
fenestra ovalis and rotunda in the lymph in the labyrinth, as well as along 
the chain of bones, and impressed the nerve end organs. This view 
of the mode of excitation of the auditory nerve seems to be the most 
satisfactory. 



{Issued separately December 31 , 1913 .) 



1913-14.] Siliceous Sponge of the Order Hexactinellida. 



23 



III. — Note on a Siliceous Sponge of the Order Hexactinellida from 
South Shetland. By Principal Sir William Turner, K.C.B., 
D.C.L., F.K.S. 

(Read December 1, 1913. MS. received December 2, 1913.) 

The specimen was presented to me by Mr G. Millen Coughtrey, who 
obtained it in Admiralty Bay, South Shetland, lat. 62° S., and long. 58° W., 
in 1912. It was procured in about 20 fathoms, and was brought to the 
surface when the ship’s anchor was weighed. It consisted of white, delicate, 
thread-like spicules collected into two tufts or bundles. At the first glance 
the threads might easily have been mistaken for white hair, but they 
would not burn ; neither were they calcareous, for they were not acted on 
by mineral acids. From their vitreous appearance they were obviously 
siliceous and indeed were not unlike spunglass. Their aspect and com- 
position led me to regard them as belonging to a siliceous sponge, but the 
body of the sponge was wanting. In its absence one had to rely on the 
characters of the tufts and spicules in attempting to determine the genus 
of the sponge. 

One tuft was about 40 cm. (16 inches) long, and 3J cm. at its greatest 
transverse diameter. The thread-like spicules were compacted and inter- 
laced together at the proximal and mid parts of the tuft, but at the distal 
end it was somewhat dishevelled. It contained many hundred spicules 
and seemed as if it had belonged to one sponge. The smaller tuft was not 
so compact and might possibly have been divided into two parts, one for 
each of two smaller sponges. 

The threads were the basalia or basal spicules of the sponge, which 
had grown downwards from the base of its body and had penetrated the 
mud on the floor of the sea in which the sponge lived. In weighing the 
ship’s anchor the tufts of basal spicules had been drawn up at the same 
time. The spicules were so brittle that it was difficult to pick a single 
one out of the tuft without breaking it, but with care I obtained examples 
30 cm. (12 inches) long. The spicules were smooth on the surface, 
translucent, and the transverse diameter ranged from 35 to 92 jm. In 
many of the smaller sizes the appearance of a narrow canal in the long 
axis of the spicule was seen, but in the wider spicules no structural 
differentiation was observed. One end of the spicule was frequently 



24 



Proceedings of the Royal Society of Edinburgh. [Sess. 

attenuated to a fine point, though often it was broken abruptly; the 
opposite end was sometimes broken, at others it terminated in a very 
minute knob (scarcely visible to the naked eye), which, when magnified, was 
seen to be the rounded end of the basal spicule from which four hook- 
like processes equal in length arose ; they were recurved in their direction, 
almost parallel to the long axis of the spicule, and formed an anchor-like 
arrangement which assisted in fixing the sponge in the mud (figure). 

A close examination of the tufts showed that a number of the spicules, 
more especially near the proximal part of the tuft, had attached to them 
globular blackish specks, 300 to 320 ju in diameter, which contrasted in 
colour with the white spicules. Under low magnification they looked like 
very minute grains, and had with strong transmitted light a greyish-blue 




Anclior-like end of basal spicule of siliceous sponge, South Shetland. 



tint. Neither Canada balsam nor treatment with acetic acid and glycerine 
made the centre translucent, but the thinner periphery permitted greyish - 
blue-tinted siliceous microscopic flakes or scales to be seen, which, when 
superimposed on each other, gave opacity to the object. Owing to their 
hardness and brittleness, attempts failed to make sections through them. 
They seemed to be aggregations of siliceous plates attached to the spicule, 
the purport of which was difficult to explain. 

A brown substance was occasionally seen to surround some of the basal 
spicules in the proximal part of the tuft. The largest example was 6 mm. 
long and was fusiform. From its structure it was essentially a fragment 
of the body of the sponge which had adhered to the basal spicules. In 
part it contained nuclear-looking bodies embedded in a granular protoplasm, 
but a number of ray-like spicules were also present. Many of these were 
four-rayed tetracts, which radiated horizontally from a common centre, and 
the largest specimens measured 0*5 mm. between the tips of opposite rays. 



25 



1913-14.] Siliceous Sponge of the Order Hexactinellida. 

Others were much smaller, 0‘2 mm. between their tips, and in many five or 
six rays could be seen, one or two of which had been broken across at or 
near the common centre ; the type, therefore, was hexact. In the middle of 
the centre was a very minute circle, from which a line passed along the axis 
of each ray almost to its tip. The rays were sometimes smooth, but more 
usually slightly roughened near the tip and faintly serrated at the sides. 
Mingled with the ray-like spicules were numerous disc-shaped Diatoms, 
which varied in their dimensions from 77 to 96 /u across the face of the 
disc. They had doubtless lived in the mud in which the basal tuft had 
been anchored. 

As the siliceous sponges have been described by Professor F. E. Schulze 
in an elaborate memoir in his Challenger Report on the Hexactinellida,* 
I have examined the text and figures so as to identify, if possible, the 
species from the characters presented by the basal spicules. The length 
and thickness of the tufts and the number of spicules varied materially in 
different genera and species, but in the genera Hyalonema and Pheronema 
species existed in which the basal tuft of spicules attained a considerable 
length. Schulze gave as a character of Hyalonema a tuft consisting of 
long and strongly developed basal spicules which projected downwards 
from the centre of the lower end of the body, and the spicules themselves, 
either wholly, or for the most part, had four-toothed anchors. He stated 
that in H. sieboldii the total length of the body and tuft varied from 50 
to 80 cm., and as the body occupied 10 to 15 cm. of that length, the basal 
tuft varied from 30 to 60 cm., and broke up at the lower end in a brush-like 
manner. This species inhabits the seas of Japan. In H. affine the tuft 
was 47 cm. long, but only 8 mm. broad. Wyville Thomson dredged in the 
sea north of the Butt of Lewis, from a depth of 450 to 500 fathoms, 
Hyalonemata in which the root tuft measured 40 cm. or more. In Phero- 
nema carpenteri, obtained in the sea north of Scotland, as well as off the 
coast of Brazil, a number of slender tufts, only 1 to 2 mm. in breadth, the 
spicules of which were 30 to 40 cm. long, interlaced abundantly in the felt- 
work of the basal tuft. Wyville Thomson considered that in the larger 
specimens the tufts may measure several decimetres. Schulze stated that 
other species of this genus also possessed long basal spicules. 

Schulze has figured Numerous examples of four- and six-rayed spicules 
in the bodies of the sponges in the Hexactinellida group. In my specimen 
the rayed spicules found in the basal tuft did not properly belong to it, 
but had accidentally become intermingled with the basal spicules. Schulze 
specially referred to the lower end of the body of Hyalonema as containing 

* Yol. xxi. part 53, 1886. 



26 



Proceedings of the Royal Society of Edinburgh. [Sess. 

four-rayed, tetract spicules. In the length of the tuft and in the numerous 
spicules which composed it, this sponge had also affinities with Hyalonema, 
though none of Schulze’s figures had so bulky a tuft. Hyalonema sieboldii , 
however, seems to be the sponge which most closely corresponds with it in 
this particular. 

Two other questions of interest arise out of this specimen, viz. : the 
locality and the depth from the surface. Schulze, in his map, showed the 
distribution of the order Hexactinellida, and localised a small species, 
Rossella antarctica (Carter), obtained by Sir James Ross in 1839-43, as far 
south as lat. 74*5°, at a depth of 300 fathoms ; also a small species, Polyrhabdus 
oviformis (Schulze), obtained by the Challenger in lat. 62*26°, in 1975 
fathoms. With these exceptions no other specimen of this order, which 
from the size of the basal tuft was obviously a large species, had previously 
been obtained so near the Antarctic circle as 62° S. In his chapter on the 
bathymetrical distribution of the Hexactinellida, Schulze gave several 
species as dredged from a depth at and near 100 fathoms ; but the depth 
of only 20 fathoms, given by Mr Coughtrey for the South Shetland specimen, 
localises Hyalonema in a shallower sea than had previously been recorded. 



( Issued separately December 31 , 1913 .) 



1913-14.] Factorable Minors of a Compound Determinant. 



27 



IV. — Some Factorable Minors of a Compound Determinant. 
By Professor W. H. Metzler. 

(MS. received April 17, 1913. Bead November 3, 1913.) 



If we start with a determinant A of order n, and, using exclusive umbral 
notation, take the minor 



Mee 



(n\m\k) 

a 1 

(n | m | k) 



(n | m | k) 

a 2 

(n | m | k) 



(n I m | k) \ 
a x \ 

(n\m\/c) L 

a \ / 



m k 



of the (n — 7c)th compound of A, Sylvester * has shown that 



M = A 






(n | m) 
( n | m) 






. (A) 



Besides this, Muir j- has considered another type of minor which breaks 
up into factors. It may be obtained from M by putting k = m— 1, and in 
place of the combinations — 1), . . . 1) indicating the 

a 1 am 

selections of rows for the elements we take the combinations 12 . . . m— 1, 
23 . . . m, 34 . . . m+1, . . . mm + 1 . . . 2n — 2, where for definiteness 
of statement we suppose a = 1, and (n \ m) = 12 . . . m. Thus the theorem 

a 

given in Muir is 



12 ... m- 1 




23 ... m 




mm + 1 . 


. . 2m -2 


(n\m\m — T) 
\ l i 




(n | m | m - 1) 
1 2 




(n m 

l 


i m — i) 

m 





23 ... m + 1 




34 ... m + 2 


A . 


( n | m) 




(n | m) 




l 




l 



m . . . 2m — 3 

( n | m) 

l 



(B) 



In both these theorems the combinations indicating the selection of row 
numbers are definite. In Sylvester’s theorem they are the same as the 
selection of the column numbers. In Muir’s the first one is the same, and 
the rest may be obtained by a definite sliding process. 

The object of the present paper is to show that there are a large number 
of other minors which break up into factors, and to give a general theorem 
(C) which includes these two as special cases. 

Theorems (A) and (B) are readily proved by the method used by the 

* Philosophical Magazine , 1851. 
t A Treatise on Determinants , Art. 93. 



28 



Proceedings of the Royal Society of Edinburgh. [Sess. 



author in 1897.* Starting with a particular case of the general theorem 
(C), where m = 5 and k = 3, and using a similar method, we have on 
multiplying 



1 2 3 

4 5 
4 5 



M= 

% 



— 4 


--5 


-34 


1-35 


1-45 


2 3 4 


2 3 5 


2 4 5 j 


|3 45 


\ 


1 2 4 


1 2 5 


1 3 4 


13 5 


1 4 5 


2 3 4 


2 35 


2 4 5 | 


345 


) 



3 5 


i 3 4 


2 5 


2 4 


2 3 j 


1 5 


1 4 


13 


1 2 


\ 


3 5 


3 4 


2 5 


2 4 


2 3 


1 5 | 


1 4 


13 


1 2 


) 



where the positions indicated by the dashes in M may be filled with any 
numbers from the set 12 ... n, as long as (1) no two numbers in the 
same element are alike, for in that case every element in that row of M 
would be zero; (2) the row numbers in the fth row of M and the com- 
plementary with respect to m of the column numbers in the fth column 
of M have no numbers in common, for if they had then the corresponding 
element in the principal diagonal of the product would be zero, and 
therefore the product zero; the product 



M.N = A 10 . 



45 




— 3 4 51 


--345 




-23451 


-2 3 45 




-2345i 


1 2345 


i 1 2 3 4 5 




12345’ 


1 2 3 45 




12345’ 


1 23 45 




12345’ 


1 2 345 



N = A 6 . 



1 2 3 4 5 
1 2 3 4 5 



45 




- - 3 4 5 


--345 




- 2 3 4 5 




- 2 3 4 5 




- 2 3 4 5 


1 2 3 4 5 




1 2 3 4 5 


'12345 




1 2 3 4 5 




1 2 3 4 5 




1 2 3 4 5 



For the product has every element on one side of the principal diagonal 
zero, and therefore it equals the product of the elements along the principal 
diagonal. 

By Sylvester’s theorem 



and dividing out the common factor from both sides we have 



M = A 4 



where of course the numbers in the places indicated by the dashes are the 
same with which we started in M. 

It will be observed that the 4 in the row numbers of the second row 
of M, the 5 in the third row, the 3 and 4 in the fourth, the 3 and 5 in 
the fifth, etc., are what make all the elements on one side of the principal 
diagonal of the product vanish and the minor break up into factors. This 
is true independent of the numbers (under the restrictions named) in the 
places indicated by the dashes. 

* Metzler, “Compound Determinants,” American Journal of Mathematics , vol. xx. 
No. 3. 



29 



1913-14.] Factorable Minors of a Compound Determinant. 

The row of M which has the three arbitrary row numbers is the same 
(viz. the first) as the column of M which has the column numbers 12 3. 
That is, the three arbitrary row numbers are associated with the column 
numbers 12 3, and it is obvious that they might have been associated with 
any of the ten combinations of the numbers 1 2 3 4 5 taken three at a time. 
Thus, for instance, associating them with the combination 2 3 4, we have 
the minor 



( 


— 


--5 


1 -- 


-45 


1-4 


1-5 


3 4 5 


1 3 4 ; 


1 35 


145 


\ 


2 3 4 


2 3 5 


12 3 


2 45 


1 2 4 


125 


3 4 5 


134! 


1 35 


145 



1 5 




1 — 4 5 1 


1 — 4 5 


1-345 




1-345 




1-345 


1 2 3 4 5 




12345* 


1 2 3 45* 


1 2 3 4 5 




1 2 3 4 5 




1 2 3 4 5 



If in M we put in the place of the dashes the same numbers as those in 
the column numbers with which they are associated, the six factors other 
than A 4 are all equal, and we have Sylvester’s theorem. 

If 1c = 4 and we take the minor 



12 34 
12 3 4 



123- 
12 3 5 



1 2 -- 
1245 



1 

13 45 



2 3 4 5 



M= 

which equals 

A • 

and put in the place of the dashes 8, 7 8, 6 7 8, 5 6 7 8, respectively, so that 

MW 



1 2 3 4- 




12 3 — 


1 2 j 


1 


1 2 3 4 5 




1 2 3 4 5 


1 2 3 451 ' 


1 2 3 4 51 



1234 

1234 



1238 
12 35 



1 2 7 8 j 116 7 8 
1245 1345 



5 6 7 8 
2 3 4 5 



we have 



M = A • 



1 2 3 4 8 




1 2 3 7 S 


[1 2 6 7 8 




1 2 3 4 5 




1 2 3 4 5 


* 1 2345 





1 5 6 7 8 
1 2 3 4 5 



which is an example of Muir’s theorem. 

In the general case the theorem is simple, though its statement is a 
little cumbersome. 

Take any one of the — A combinations (n\m \ k), (n\m\ Jc), . . . 

a 1 a. 2 

(n\m\ k), say the /3th or (n\m \ k) to start with, and arrange the set into 

a \ a /3 

groups as follows : — 

1st group containing 1 combination consisting of (n | m 1 Jc). 

a (3 

2nd group containing (m — k) l combinations, consisting of those which 
have in common the first (Jc — 1) only of the numbers of (n | m 1 1c). 

a £ 



30 



Proceedings of the Boyal Society of Edinburgh. [Sess. 

(h l)st group containing (m — Jc + h— 1) A combinations, consisting of 
those which have in common the first (k — h) only of the numbers 
of (n\m \ k). 

a jS 



(/c + l)th and last group containing (m— 1)* combinations, consisting of 
those which do not contain the first number in (n\m\ k). 

a J8 

Let 

(n\m\tc\Ic-h)(c m ), (* = 0 , 1 , 2 , . . . (m-k + h- 1 ) - 1 ) 

a 0 1 1 h 

represent the combinations of the (/& + l)st group. By giving h in this 
the values from 0 to k, it will represent the combinations of each group. 

Let the first combinations in the 1st, 2nd, . . . (& + l)th groups, ar- 
ranged in this order, be represented by 



(n | m | k ), (n \ m \ k ), . . . (n\m\k) i 
Po Pi a Pk 



respectively, and let 
p — 1 k 

a FT Tal 

0 0 



(n \m\ k ) 

a p h +i 

(n\m\k\k-h)(c W ) 

a P 1 1 



(p = (m-k + h — 1 ) ft ) 



represent the determinant whose elements along the principal diagonal 
arranged in the above order are 



(n | m | k) 

a 1 




(n\m\ k) 

a 2 




(?i | m | k) 

a \ 


(n | m k) 

a 1 


> 


(■ n | m | k) 

a 2 




(n\m\k) 

a \ 



Then the determinant 

(n | m | k ) 



p - 1 k 

d^a in III 

0 0 







(n | m) 

a 

(b< k - h) )(+ ) )(n\m\ k ) 

a P h +i 



A (m_1 k (C) 



where (b^ ll) ) represents any set of (k — h) of the numbers 1 2 3 ... n, as 
long as (1) (bf h) )(c^) has no two numbers alike; and (2) no numbers 
in (Jbf h) ) and (n | m | k ) are alike. 

a p +t 
h 



1913-14.] Factorable Minors of a Compound Determinant. 31 



For if we multiply D by 



p - 1 k 

A ITT IM 

0 0 



/\(n\m\ k ) 
/ a Ph +i 

\ \ {n\m\ k) 

\ 1 a ft h +i 



which by Sylvester’s theorem is equal to 



^ (n | m) 3 

a 

(ji | m) 



the resulting determinant will have every element on one side of the 
diagonal zero, and therefore equal to the product of the elements along the 
diagonal. Dividing out the common factor from both sides, we get the 

o o 7 o 

result given. 



Syracuse University, 
March 1913. 



(Issued separately December 31, 1913.) 



32 



Proceedings of the Royal Society of Edinburgh. [Sess. 



V. — The Theory of Bigradients from 1859 to 1880. 

By Thomas Muir, LL.D. 

(MS. received June 9, 1913. Read November 17, 1913.) 

My last communication in reference to the history of bigradients ( Proc . 
Roy. Soc. Edin., xxx. pp. 396-406) brought the record up to the year 
1859. The present paper continues it to the year 1880. 

Bruno, F. Faa di (1859). 

[Theorie Generale de l’Elimination, .... x + 224 pp. Paris.] 

In his section on the highest-common-divisor (pp. 47-52) Bruno, denoting 
the r th Sturmian remainder of 

%x m + a^x m ~ x + • • • •, & 0 a? m_1 + b 4 x m ~ 2 + • • • ■ 

by R r , finds for it the expression 




where \ r and R r /A r are the “ allotrious factor ” and “ simplified residue ” of 
Sylvester (1853). He must, however, have overlooked the question of sign, 
for the example which he gives, namely, 



1 


% a i a 2 


X 2 + 


a 0 <h a B 


x + 


a 0 a x a 4 




b 0 \ 5 2 




K b l h 




bo \ 


( 


b 1 




. b 0 5 2 




CO 

hO 

o 



as the first Sturmian remainder of 

+ a 4 x 2 + • • . + a 4 , b 0 x s + b ^ + b 2 x + b z 
is incorrect in this particular. 



33 



1913-14.] The Theory of Bigradients from 1859 to 1880. 

In the section on the properties of the resultant (pp. 68-81) he recalls 
Richelot’s theorem of 1840, that if w be a common root of the equations 

a^x m + apc m ~ x + • • • = 0 , b^x n + \x n ~ x + • • * = 0 

whose resultant is R, then we have 



0R , 


0R . 


. ?R 


da Q ' 


0a x 


* da m 


0R 


. 3R . 


0R 


3 V 


1 06 x : ' 


' ' '' M n 



This is not brought forward as a theorem in determinants, hut for com- 
parison, when n = m, with Jacobi’s theorem of 1835 to the effect that the 
■signed primary minors associated with the elements of any row of Bezout’s 
condensed eliminant 



■are proportional to 



a o b i 






^0^2 I ! ®o^3 I "t" I ^l b 2 



m 



w m x , w m 2 , . . . , IV , 1 . 



In the section on common roots (pp. 81-84) he obtains such a root when 
it is solitary by taking any one of these three series of proportionals and 
dividing one member of the series by the member immediately following. 
When the number of such roots is lc he has recourse to the Sturmian 
remainders previously found, stating for comparison Lagrange’s set of 
conditions : * 



R = 0, 




02R _ 0 *-^ 

da 2 m ’ ’ ba k ~ l 



0. 



Trudi, N. (1862). 

[Teoria de’ Determinant:, .... xii + 268 pp. Napoli.] 

To Trudi is due the first methodical exposition of bigradients, a nineteen- 
page chapter of the first part ( Teoria ) of his text-book being specially 
devoted to them, and several chapters of his second part (Applicazioni) 
making constant use of them. 

The nineteen-page chapter or section (§ xi., pp. 94-112) bears the head- 
ing “ Matrici e determinanti a due scale.” It contains, first of all, careful 
explanations of the various expressions which he finds necessary to use in 

* Lagrange. Reflexions sur la resolution algebrique des equations. Nouv. Memoires 
. . . Acad. . . . Berlin , 1770, 1771 : or (Euvres completes , iii. pp. 205-421 (227-229). 

VOL. XXXIV. 3 



34 



Proceedings of the Royal Society of Edinburgh. [S 



ess. 



a special sense while dealing with such determinants ; for example, scala , 
scala, di grado r, scala diretta, scala inversa, scala completa, etc. He next 
gives an account of the simple properties of bigradient arrays, or, as he calls 
them, two-scale matrices, and introduces a notation for them, writing 

j { a o)r 

I (\)s 

to denote the bigradient array in which the elements a 0 , a v . . ., a m are 
repeated r times, and the elements b 0 , b v . . ., b n are repeated s times, a 0 and 
b 0 when furthest to the left being in the first column, and a m and b n when 
furthest to the right being in the last column. Clearly, the notation would 
have been less imperfect if written 



(“o> • 


• • ) ^"m)r 1 


! (&», • 


. . , u ! 



For example, the bi gradient array 



°0 


cq 




«8 


<q 


a h 


“6 


a 7 


• 






a o 


«1 


a 2 


a 3 


a i 


«5 


«6 


a 7 




• 




a 0 


<q 


a 2 


«3 


a i 


°5 


a 6 


a 7 












b o 


h 


K 
















h 


\ 












• 




K 


\ 


h 












h 




\ 


h 


h 












h 


^2 


h 


h 










K 


h 




h 


K 













might with fair appropriateness be denoted by 



(«o> • 


• • j a r)s 


1 (K ■ 


• • > ^4)6 



the only weak point then being that the introduction of the 6 is uncalled 
for, on account of the necessary equality of m + r and n + s, either of which 
specifies the number of columns in the array. It is a convenience, however, 
to have both the outside suffixes 3, 6 in front of us, because their sum 
gives the number of the rows, a sum we should otherwise have to know 
from m + 2r — n. Instead of all the determinants of such an array being 
viewed, as hitherto, of equal prominence, Trudi only concerns himself with 
the first two of the ten, namely, those which have in common the first eight 
columns of the array. These n — r+ 1 determinants he designates not very 
happily “ the successive determinants of the array.” The name “ principal ” 
which he gives to the first determinant of all may be advantageously 
translated “ leading.” 



35 



1913-14.] The Theory of Bigradients from 1859 to 1880. 

The number of bigradient arrays associated with the two sets of 
elements 

’ ' • ’ K ^1’ • ' ’ ’ 

is evidently n : thus, in the case where m,n = 7,4 the arrays are 



(%< • • 


• . «r)x 




( a o> • • 


• > ^7)2 




(®o > . . 


. , oq) 3 




«o>* ■ 


. . , & 7)4 


(K ■ ■ 


•.M4 


f 


■ ■ 


• . *4)5 


> 


(K ■ ■ 


• 5 


I ? 1 


K • • 


■ ..sa 



the last, where r = n, being square, and therefore preferably written in 
the form 

I (« 0 » • • • » I 

I (&0. • ' • 5 ^4)7 I ’ 



These and other preliminaries being settled, he is in a position to deal 
with an important theorem on the subject of what we may call the con- 
densation of a bigradient array. The proof given is, unfortunately, not 
at all so simple as it might have been. We shall therefore substitute for 
it one of our own, which Trudi himself would probably have devised had 
he been aware of Cayley’s work of 1845. Taking, first, a case in which 
m = n, say the case 



a 0 


“1 


«2 




*4 


• 






a 0 




“2 


«B 


a 4 








«o 


a i 


a 2 


«3 


“4 








\ 


h 




*4 








h 


h 


^4 




% 


h 


K 


h 


h 









(«o> • • 


. , a 4 ) 3 


or 


00. • • 


• 5 ^ 4)3 



we multiply the determinant 



1 














1 






0 
r-c> 

1 








1 


~h 


-h 


~ ^2 








a 0 


cq 


a 2 










a 0 


a i 












a 0 



by the given array in column-by-column fashion, obtaining {Hist., ii. p. 34) 









^0 ^2 


a B 


«4 












a 0 


a 2 


«3 


« 4 


• 


\ («0. • • 


. . , a 4 )g 




. . a 0 


a i 


a 2 


«8 


a 4 


1 00. • ■ 


■ • . £ 4)3 


r 




1 “(A 1 


1 «0 6 2 1 


KVI 


1 a A 1 










1 <*A 1 


I S 6 3 1 + 1 a A 1 


1 «0 6 4 1 + 1 « A 1 


l | ! 










«0 & 3 1 


1 «o 6 4 1 + I af 3 I 


1 «A 1 + 1 ,% & 3 i 


1 « 2 & 4 1 1 



36 



Proceedings of the Royal Society of Edinburgh. [Sess. 

Of the seven identities included in this the first two are Trudi’s, and these 
he writes in combination, thus — 



a o 


a 4 


a 2 




‘h 






• 


a o 


a j 


« 2 


a s 


a 4 








% 


a \ 


a 2 


a 3 


a 4 








h 




b B 


b 4 




b» 


h 


h 


h 


K 




\ 


h 


h 


b s 


b\ 







1 a o h i 1 


1 a 0^2 1 


1 a 0^3 i 


1 %b i \ 


1 a J , 2 1 


1 a 0^3 I 4* 1 a i^2 ! 


1 Vk 1 + 1 a A 1 


I «A 1 


1 a (fo 3 j 


| a (fi 4 1 4 | | 


| a x b 4 1 + ! a. 2 b B j 


1 «2 & 4 1 1 



meaning thereby that the determinants got by leaving out the 7 th column 
on the left and the 4 th on the right are equal to one another, and also 
those determinants got by leaving out the 6 th column on the left and the 
3 rd on the right.* 

He then draws attention to the fact that the two-line determinants 
involved in the array on the right are principal minors of the array 

d rv CL-y Cic) Clo d* 



and he formulates a mnemonic rule like Sylvester’s {Hist., ii. p. 340) for 
the formation of the condensed array. His own illustrative examples are 



a 


b 


c 


d 




. 










. a 


b 


c 


d 






au - bt 


av - d 


ax - dt 




a 


b 


c 


d 






ax — dt 














= 


av - d 




bx - du 


. 


t 


u 


V 


X 






+ bv — cu 




. t 


u 


V 


X 






ax- dt 


bx - du 


cx - dv 


t 


u 


V 


X 
















a 


b 


c 


d 
















a 


b 


c 


d 




au - bt 


av - d 


ax - dt 






t 


u 


V 


X 




av — d 


ax - dt 


bx — du 




t 


u 


V 


X 








+ bv — cu 






a 


b 


c 


d 


_ 


|| au - bt. 


, av — d, 


ax - dt | 




t 


u 


V 


X 











* With Cayley the assertion 



Ii % 


« 2 


a B 


a 4 1 


= \\ x i 


x 2 


x 3 


x 4 


II \ 




b 3 


\ II 


II Vi 


V2 


V 3 


Vi 



included 6 equations, whereas with Trudi it only includes 3, namely, the first 3 of Cayley’s 
6 : and with Cayley the assertion 



a l 


a 2 


C*3 


a 4 




x i 


x 2 


Xo j 


*1 


b 2 


h 


\ 


— 
















! Vi 


V2 


y 3 1 


C 1 


C 2 


C 3 


c 4 











was meaningless, whereas with Trudi it includes 2 equations. Since in the former case 
Trudi’s 3 equations are known to necessitate the other 3, there is clearly no good reason for 
refusing to profit by the new usage. What is common to any two arrays which Trudi may 
equate is the excess of the number of columns over the number of rows : and evidently if 
his excess be 5, the number of included equations is 5 + 1. 



37 



1913-14.] The Theory of Bigradients from 1859 to 1880. 



where each array on the left is got from the one that precedes it by 
deleting the first row, the first column, and the last row ; and each array 
on the right by merely deleting the last row. It is noted that the leading 
determinant of the condensed array is axisymmetric. 

Lastly, it is pointed out that cases where m>n present almost no 
additional difficulty, as they are readily brought under the foregoing. 
Thus, if the case be 



we have only to take 



I (a, b, c, d, e, f) 2 I 
I (t, u, v) 5 j 

a b c d e f 

0 0 0 t u v 



for our generating array and proceed exactly as before, the results being 



a 



b 


c 


d 


e 


f 




r 










a 


b 


c 


d 


e 


f 








at 


au 


av 










t 


u 


V 






at 


au + bt 


av + bu 


bv 








t 


u 


V 




= 


at 


au + bt 


av + bu + ct 


bv + cu 


cv 


a z 




t 


u 


V 








au 


av + bu 


bv + cu 


cv + du — et 


dv - ft 




t 


u 


V 










av 


bv 


cv 


dv - ft 


ev - fu 





u v 



a b c d e f 

t u v 
t u v . 

t u v . 

t u v 









t 


u 


V 






t 


u 


V 




= 


t 


u 


V 








au 


av + bu 


bv + cu 


cv + du — et 


dv - ft 




av 


bv 


cv 


dv -ft 


eu —fu 


- 






t 


u 


V 




• 


t 


u 


V 






t 


u 


V 




. 




au 


av + bu 


bv + cu 


Cv + du — et 


dv -ft 



The requisite division by a 3 (in general a m n ) may be performed by 
removing the a’s one at a time, or by using the divisor in the form 

a b c 
a b . 



Another theorem of a similar kind but introduced for a different 
purpose, namely, for dilatation rather than condensation (pp. 129-131), is 



(*o 



K), 



(-r 



• • • , Or 



38 Proceedings of the Royal Society of Edinburgh, 

where the c s are determinants defined by the postulated identity 



[Sess. 



a {) x'" + • • • 
b^x n + • • • 



q 0 x r ‘ 



+ ... Hr 



b 0 x" 



(see under Recurrents ) and where a- = r + 1 + f (m — n)(m — n — 1). For 
example, when m = 5, n = 4, r = 2 the identity is 

















a o 


a l 


Ctcy 


® 3 


a 4 


a 5 






\ 


b 


h 


b 


b 


• 






a 0 


a i 




a s 


a 4 


°5 






\ 






b 


b 


_ (-1)* 






a o 


a , 

b 


b 

b 


« 3 
b 
b 


«4 

&4 


«B 

7, 




c o 


c o 

C 1 


C 1 

C 2 


C 2 

C 3 


C S 


V 






\ 




c o 




C 2 


C 3 










b 




b 


b 


b 




















b 


b 




b 


b 









Trudi’s proof consists in evolving the second member from the first, but 
here again it is simpler to use Cayley’s multiplication-theorem of 1845. 
Thus, taking the second array as multiplier and the determinant 

1 ..... 

1 

1 .... 

. . - qi 1 . . . 

-0i "0o * 1 • • 

- 01-00 • . . 1 . 

- 00 1 



as multiplicand we at once find the product to be 







c o 


c ] 


C 2 


C 3 


• 










c o 


C 1 


6 2 


C 3 












C 0 


C 1 


C 2 


C 3 








b 




b 2 


h 


b 




. 


b 


b 




h 








b 


b 


b 


\ 




• 






b 


b 


b 


\ 









which is equal to 



c 0 


C 2 


CO 






. c 0 


C 1 


^2* 


C 3 




. 


c o 


C 1 


C 2 


C 3 


. \ 


h 


b 


^3 


b 


\ \ 




b 


V 





(b ■ 


■ • ^ 4)2 


( c o • ■ 


• • 5 ^ 3)3 



as was to be proved. 



39 



1913-14.] The Theory of Bigradients from 1859 to 1880. 

The use to which this second theorem is put (pp. 132-137) is in 
connection with the division-process for finding the highest-common- 
divisor of two integral functions, and, in particular, with the modification 
of the said process employed by Sturm in obtaining his so-called 
“remainders.” From the general theorem* connecting dividend, divisor, 
quotient, and remainder we know that the coefficients of the first remainder 
in such a process are proportional to the successive determinants of a 
bigradient array composed of the coefficients of the dividend and divisor. 
We thus also know that this remainder having been made the divisor and 
the previous divisor the dividend, the new remainder must be expressible 
in like fashion. In the second bigradient array thus arising, however, one 
of the two sets of elements is complicated, being in fact the successive 
determinants of the previous array : and what Trudi’s “ dilatation ” theorem 
enables us to do is to supplant it by another array whose elements are 
simply the coefficients of the original functions. In this way the theorem 
finally reached is : The coefficients of the r th remainder R r arising in the 
course of the performance of Sturms division-process on 

a^x m + . . . + a m , b 0 x 11 + ... + b n 

are equal to the successive determinants of the array 



(a 0 , . . 


■ , a,n)r 


(b 0 . ■ . 


.,K) \ 



divided by the product of the squares of the first coefficients of all 
the preceding remainders and by b 0 m-n+1 and by the sign-factor 
( _ xive r th remainder, when divested of the threefold divisor 

here specified, a r say, Trudi follows Sylvester in calling the residuo 
semplificatofr and denotes by p r , so that R r = p r /a r . For example, when 
the originating functions A and B are 

ax i + bx B + ex 1 + dx + e, 
px* + qx 2 + rx + s, 



* See under Recurrents. 

t A most natural and helpful notation for such a remainder would he 

II Oo, . . . , a. m )r II ( x n ~ r ,. 1). 

II (&o, bn) II 

Thus, in the case here used for purposes of illustration, the remainders would be written 



a b 


c d e j 


(x“, x , 1), 


|| {abed 


e h II 


. p 


q r s \ 




l| (p q r 


s) 3 |l 


P <1 


r s . 1 


1 







40 



Proceedings of the Royal Society of Edinburgh. [Sess. 



the three Sturmian remainders in their “ simplified ” or disencumbered 
form are 



a 


b 


c 




a 


b 


d I 


a 


b e 




V 


2 


+ 

<M 

8 




V 


T p “H 




p s 


V 


<1 


r 




p 


<1 


s \ 


p 


<1 • 



a 


b 


0 


d 


e 


a 


b 


c 


d . 




a 


b 


0 


d 




a 


b 


o e 






V 


d 


r x + 






V 


q s 




p 


d 


r 


s 




P 


d 


r . | 


V 


d 


r 


s 




p 


d 


r 


s 



abode 
abode 
a b c d e 

p q r s 

p q r s 

p q r s 

p q r s 

the removed encumbrances being the factors 

















a 


b 


c 


2 


















P 


d 




1 




p 2 










V 


d 


r 




p 2 


a 


b 


0 


2’ 


p 2 


a 


b 


0 


d 


e 


2 






P 


d 








a 


b 


0 


d 






p 


d 


r 










p 


d 


r 


















p 


d 


r 


s 
















p 


d 


r 


s 


. 





respectively. The general expression for the factor, a r , connecting the 
simplified and unsimplified forms of a remainder is readily got (pp. 138-139) 
in Sylvester’s way by using the fact that the product a v _ x a r is equal to the 
square of the first coefficient of p r . For, this is the same as saying that, if 
we denote the first determinant of 



by D r , we have 
and these lead to 



and 



where 



j (a 0 , ... , a m ) r j| 

I (6q , . . . , & n ) || 



l 2 2 



— T)2 



= j . . . • Dt-i 

a, 



a 2ju,+l 



1 d m • • • ’ 



a 1 = (~ . b 



m—n+ 

0 



41 



1913-14.] The Theory of Bigradients from 1859 to 1880. 

An important observation made in passing is that any simplified 
remainder can be condensed into a single determinant : for example, the 
three just given are equal to 



a 


b 


ex 2 + dx + e 




a b 


A 




P 


qx 2 rx + s 


or 


• V 


B 


V 


! 1 


rx 2 + sx 




p a 


Bx 



a b c 


d ex 




a b 


c d Ax 


a b 


c dx + e 




a 


be A 


p 


q rx-rS 


or 


. . p q B 


• P 2 


r sx 




• P < 


q v Bx 


p q r 


s 




p q r s B x 2 




a b c 


d e 


Ax 2 






a b 


c d 


e Ax 






a 


b c 


d A 








V d 


r B 






• . p 


q r 


s Bx 






• V 2 


r s 


. Bx 2 






p q r 


s 


. Bx 3 


, 



where, be it remarked, the ultimate forms, namely, those explicitly involv- 
ing A and B, are Cayley’s of 1848. 

Cayley’s relation between any three consecutive ‘‘simplified remainders” 
is next given (pp. 140-142), the proof arising quite naturally and being 
mainly dependent on the equality a r _ 1 a r = Dr-i- Thus, taking the equations 
that indicate the nature of the division-process, namely, 

A = QiB-R, 

B = Q 2 Bi — R 2 

b] — Q3B2 — 1*3 

b-2 = “ B 4 



and substituting p r /a r for R r , we obtain 

cq • A = cqQj-B - pj 

a l a 2 ’ B = a 2 Q2‘Pl “ a ]*P2 
a 2 a 3 -pi = a 1 a 3 Q 3 *p 2 - cqcq-pg 

a 3 a 4’P2 = a 2 a 4Q4'P3 “ a 2 a 3'P 4 

In this way there results the general equation 

Or-lOr • Pr-a. = a r-2 a rQr’Pr-l “ a r _ 2 a r _ 1 -p r , 
Hr— 1 * Pr— 2 a r— 2 a rQr’Pr— 1 — ^r—2’Pr •> 



and thence 



42 



Proceedings of the Royal Society of Edinburgh. [Sess. 



showing that p r _ 2 and p r have different signs for any value of x that makes 
Pr^ vanish. 

Proceeding from the above-noted Cayleyan mode of expressing the 
“simplified remainders,” Trudi puts forward (pp. 145-152) another mode, 
each remainder now appearing as a sum of a multiple of A and a 
multiple of B ; or, in Sylvester’s words,* as a syzygetic function of A and B. 
For example, the three remainders above given he considers in the form 



1 



A + 



a b 

. p 



B 









p 


<1 • 




p 


q 


X 




a 


b 


c 


d 


X 


A + 


a 


b 


c 


d 






a 


b 


c 


1 






a 


b 


c 








V 


<1 










P 


q 


1 




V 


<Z 


r 








V 


q 


r 


X 


p 


Q 


r 


s 






p 


q 


r 


8* 


X 2 



and generally he writes 

Pr I U r .A + V r .B , 

where it is readily seen that as regards x 

- 1 , 



U r is of the degree r 



V, 

U r A 

y,b 

and where, as we know, 

Pr 



m — n + r 
m + r - 1 
m + r 



h 



r— 1 f 



n — r . 



Observation also shows that the coefficients of the highest powers of x in 
U r , V r are H^D^, afi r _ x respectively. By substituting the new forms 
for p r _ 2 , p r _ v p r in Cayley’s relation 

By— l * Pr— 2 Ct T _ 20 t T Q r * Pr — 1 “t ' p r 0 , 

there is obtained 

(D^Lj • U r _ 2 — a r _ 2 a r Q r ■ U r _ 1 + D^_2 • U r )A 

+ ( • V r _ 2 — a r _ 2 a r Q r • V r _ x + D^_ 2 • V r )B = 0 ; 

and, as Trudi proves that this can only hold when the coefficients of A and 
B vanish, it follows that each of the two series of functions 

B"o 5 1^1 5 • • • 5 B"n+1 5 V 0 , Y"i , . . . , y n+ l 



* It is worth noting that it was in this connection that the word “ syzygetic ” was first 
used, the full title of the memoir of 1853 (which clearly had considerable influence on Trudi) 
being “ On a theory of the syzygetic relations of two rational integral functions, comprising 
an application to the theory of Sturm’s functions, and that of the greatest algebraical 
common measure.” 



1913-14.] The Theory of Bigradients from 1859 to 1880. 43 

has one of the Stnrmian properties which the p’s have been shown to 
possess. 

As regards the highest-common-divisor (pp. 142-144) his result is : 
In order that two functions may have a common divisor of the k* /l degree, 
it is necessary and sufficient that the first determinant of each of the last 
k of their bigradient arrays shall vanish: and, when this holds, the 
coefficients of the divisor in question are the successive determinants of 
the (n — k) <A array. For example, the functions being 

cLqX* + ape 1 + . . . + « 8 , bpx b + b Y x^ + ... + b b , 
their bigradient arrays are 



(« 0 . • • 


• > a s)\ 


1 (« 0 . • ' 


• • > “3)2 


1 ( a o > • • 


• . «s)j 




(«o . ■ • 


• ’ ^3)4 




(«<>>•• 


a 

00 

Cr< 


ft,,-. 


■ > h) 


, life,- 






• , h) 




(V- 




) 


(V-- 


• . h) 



and the proposition states that if the first determinant of each of the last 
three arrays vanishes, the functions have the common cubic factor 



(<*o> • 


X 


(60. • 





At a later stage (p. 151) there is given the supplementary proposition 
that the quotients resulting from dividing A and B by the said highest- 
common-divisor are, save for an unimportant factor in each case, the 
coefficients of B and A in Trudi’s form of the (n — k + iy /l “ simplified 
remainder ” — that is to say, are V n _* +1 and U n _ fe+1 as before defined. 

The closely related question concerning the common roots of two 
equations he deals with at length in a section devoted to elimination 
(pp. 161-178). Starting with the proposition that, u and v being integral 
functions of x, uA-f-tB must vanish for any common root of the equations 
A = 0, B = 0, he next points out that u and v may be so chosen as to make 
uA + tB of a low degree in x, even of the degree zero. In the latter 
extreme case uA + vB must contain the eliminant as a factor, and if in 
addition it be of the proper degree in the coefficients of A and B it is the 
eliminant pure and simple. Attention is then called to the fact that the 
division-process for finding the highest-common-divisor of A and B, or the 
Sturmian modification of this process, supplies a series of pairs of functions 
like u and v, and in particular that the last ££ simplified remainder ” D n , as 
satisfying all the requirements mentioned, is the eliminant. The condition 
for the existence of more than one common root is investigated in like 
manner. If the number of the roots in question be h, the degree-number 
of wA + tB cannot be less than h Founding on this, it is asserted that 



44 



Proceedings of the Royal Society of Edinburgh. [Sess. 

functions of the form uA-ffB whose degree-number is less than k must 
vanish identically, and that therefore in particular the last k “ simplified 
remainders” of A and B must so vanish. In the next place, proof is 
adduced that the vanishing of these remainders is equivalent to the vanish- 
ing of their first coefficients : and finally, there is reached the following 
variant to the above proposition regarding the highest-common-divisor : 
In order that the equations A = 0, B = 0 may have k common roots, it is 
necessary and sufficient that D n , D n _i, . . . , D n _ k+1 vanish : and, this being 
the case, the equation of the said common roots is p n _ k = 0. The fact that 
the vanishing of the first coefficients of the “ simplified remainders ” implies 
in each case the vanishing of all the coefficients following the first is merely 
commented on in passing. Attention, however, is more fully drawn to the 
important fact that the existence of the condensation-theorem makes it 
possible to put every proposition, which, like the foregoing, involves 
bigradients, into an alternative form. Thus, the condition that the 
equations 

x 3 + aqje 2 + a 2 x + « 3 = 0 t 
x? + b-jX + b 2 = 0 j 

may have two roots in common is, according to the said proposition, the 
vanishing of 

1 oq a. 2 a z 

1 oq a 2 ci s 
. . 1 \ b 2 

. 1 \ b 2 . 

1 \ b 2 . . 

and this by the condensation-theorem is the same as the vanishing of 



a 2 



1 



b 2 + cl-Jj 1 — a 2 
a l b 2 - a B 



oq& 2 — <^3 

Cltpbc) ? 



1 J h 

Zq b 2 -f* CL-fj-y ei > 2 | 



Bezout’s “ abridged method ” and Sylvester’s “ dialytic ” method, which 
resemble each other in involving elimination of successive powers of a 
common root, are only introduced by Trudi for purposes of corroboration. 
In connection with the former method there is noted Sylvester’s theorem * 
that the derived equations provide also an alternative way of obtaining the 
Sturmian “ simplified remainders,” the first remainder being the non-zero 
member of the first equation, the second remainder being the result of 
eliminating the highest power of x from the first two equations, the third 
remainder the result of eliminating the two highest powers of x from the 

* See Art. 5 of “ On a theory of the syzygetic relations . . .” 



45 



1913-14.] The Theory of Bigradients from 1859 to 1880. 

first three equations, and so on. In other words, if the set of equations 
derived from A = 0, B = 0 by Bezout’s method be 

c ll x m ~ 1 + c 12 x m ~ 2 + ... +c lm = 0 ^ 
c 21 x m_1 + C 22 x m ~ 2 + . . . +C 2m = 0 |- 

then the second, third, . . . “ simplified remainders ” of A and B are 



11 C l2 Xm " "f C 13^ m 3 ’ 


• • + c m 


21 ^22*^ "" "t“ ^23*^ ' 


. . + 


i r r r x m ~ 3 4- 

C 11 c 12 '13*^ ^ - 0 


• + C im 


^21 ^22 ^23*^ + , . 


• ^2 m 


C 31 ^32 C S2p C "t • • 


• +C 3 m 



Proceeding from this, Trudi then says that if the non-zero members of the 
said derived equations he denoted by Y v Y 2 . . . , the “ simplified remainders ” 
can clearly be put in the form 



V. 


c n Y, 


C 11 


C 12 Yj 




r Y i 
°21 x 2 1 * 


C 21 


c Y 

C 22 X 2 






C 31 


r Y 

c 32 x 3 



and, as by definition 



Y x — cLqB ’ 

Y 2 = (u 0 x + aq)B - (b 0 x + 6j)A , 

Y 3 = ( a ^x 2 + a x x + a 2 )B - (b Q x 2 + b x x + & 2 ) A , 



it follows that the said remainders have still another form, namely, 



0 

1 

CO 
■ ^0 




a o 


P> - 


c n 


K |A, 


| c 21 a 0 a; + oq 




C 21 


i<r 

+ 

& 

0 


C 11 C 12 a o 


P> - 


C 11 


C 12 ^0 


c 2X c 22 *t* oq 




^21 


^-'22 b 0 x -)- b j 


Cgi ^'gq a^x 2 4 - (x-^Kj 4- cl 2 




C 31 


Cg 2 b^x 2 -{- byC + b 2 



— a result easily shown, by the use of the condensation-theorem, to be in 
agreement with a previous one in which the determinant coefficients of A 
and B are bigradients. He is also careful to note that although here, as 
usual, n is taken equal to m, no real restriction is thereby made, the case 
where m>n being viewable as a case in which the coefficients of x n+1 , x n+ 2 , 
. . . , x m in B are equal to 0. For example, if the given equations be 

ax 4 + bx 3 + ex 2 + dx + e = 0 i 
qx 2 + rx + s = 0 f 



46 



Proceedings of the Royal Society of Edinburgh. [Sess. 



Bezout’s derived equations (although not in Bezout’s nor Trudi’s notation) 



are 



a bx B + cx 2 + dx + i 


\ 

= 0, 


qx 2 4- ra + s 


ax + b cx 2 + dx + e 

qx 2 + rx + s 




ax 2 + bx + c dx + e 

q rx + s 


= °. 


ax 3 + bx 2 + cx + d e 

qx + r s 


j = 0 



or, in their usual form, 



aq . x 2 + ar . x + as = 

aqx B + (ar + bq)x 2 + (as + br)x + bs = 
arx B + (as + br)x 2 + (bs + cr - dq)x + (cs - eq ) = 
asx B + bsx 2 + (cs - eq)x + (ds - er) = 



0 ^ 

0 

0 

0 ^ 



We then have for the simplified remainders of the 1 st and 0 th degrees the 
determinants 



aq 




ar , 


,x + as 


ar + bq 




(as + br ) . 


, x+bs 


as + br 


(& 


s + cr - dq ) , 


& 

+ 

Ci 

05 

1 


aq 




ar 


as 


aq ar + 


bq 


as + br 


bs 


ar as + 


br 


bs + cr - dq cs - eq 


as bs 




cs — eq 


ds - er 



being only careful to note that both of these contain the irrelevant factor 
a 2 . Trudi, however, does not point out that this factor would not have 
troubled us if we had noted at the outset that for the first two derived 
equations we might have substituted 

qx 2 + rx + s = 0 
qx B + rx 2 + sx = 0, 

thus using Sylvester’s method of derivation for the first m — n equations 
and Bezout’s for the remaining n, as Rosenhain had shown in 1844.* 

The case where B is the derivate of A receives special attention (pp. 152- 
160), the object of course being to show that the quantities D r , U r , V r are 
then expressible in terms of sums of like powers of the roots of the equation 
A = 0. The reason for the possibility of this transformation lies in the fact 
that the coefficients 

h , ^1 ) ^2 ’ • • • • 1 



* Crelle’s Journ xxviii. p. 269. 



47 



1913-14.] The Theory of Bigradients from 1859 to 1880. 

are then equal to 

^0^1 ’ ^0^2 "h ^2 ,l? 0 ’ .... 



a.Sr 



a 0 S n-l + • • • + a n-l S (i 



and that in addition we have 



(cKq , C 8 j , . . . , d n $ S n , S n _ i , 

K J 5 • • • 5 a n \ S Jl+l J S n 5 

(«0 J ^1 J • - • 5 $ S n+2 > S w+1 5 



® 0 ) = °» 

*i) = 0, 

s 9 ) = 0, 



The results arrived at are 
D, = a * 



°o °i 

Sn So 



«r-l 

S r 

s r+1 



°r+l 

S r+2 



= 0 when r>n - 1 



V,. — tto 



tl = 



. *1 


$9 




s r-l 


1 




S 2 


S 3 




. s r 


X 




! S 3 


*4 




S r+ 1 


X 2 














r+1 5 


S 0 


*1 


s 2 . . 


. . S r _! 








S l 


tS> 2 


s 3 . . 


. . 


s o 






S 2 


S 3 


S 4 • * 


. . s r+1 


S 0 X + Sj 




S 3 


S 4 


% • • 


• . S r _|_ 2 


S 0 X 2 + Sj# + s 2 


r+1- 



Here again, however, Trudi loses his opportunity from not being acquainted 
with Cayley’s multiplication-theorem of 1845, the use of which enables us 
to transform not only D r , but the whole bigradient array of which D r is the 
first determinant. In fact, it gives us for the case under consideration 
another condensation-theorem. For example, when 

A = a^x 5 + cqa? 4 + * • - + a 5 

and we consequently have to consider the four “ simplified remainders ” 



(®o > • • 


•» “5)1 1 


(x*, x\ X, 1 ), 


I (“o." 


•5 ^5)2 


(x 2 , X , 1 ), 




•> ^5)3 


|(*, 1 ). 


(«<>>•• 


•.“5)4 




•> ^4)2 ' 




II ( 6 o,.. 


•? ^4)3 






•^4)4 




!(»«,•• 


•>*4)5 



we find the condensation-results 



48 



Proceedings of the Royal Society of Edinburgh. [Sess. 



(»».'• 


• 5 a i)‘i 




• . w I 



I («o > • 


• • . “5)4 


l ( 6 , , • 


• • . *4)5 



s o 


*1 


s 2 


a 0 S 3 


a 0 s 4 


4 - ajSg 


s i 


’ S 2 


S 3 


% S 4 


a 0 S 5 


+ a l S 4 


S 2 


S 3 


*4 


<*0*5 


CLqSq 


+ “l S 5 


S 3 


S 4 


8^ 


a 0 s 6 


a 


0 S 7 


+ « 1«6 


S 0 


S 1 


S 2 


S 3 


S 4 






*1 


S 2 


S 3 


S 4 


% 






^2 


S 3 


S 4 


S o 


S 6 






*3 


8 4 


S 3 


**6 


S 7 






I *4 


S 5 


S 6 


S~ 


h 


5 





all in agreement with Cayley’s original result of 1846 (Hist, ii. pp. 162-164). 
Taking the second of these for proof, we multiply unity columnwise by the 
given bigradient array, obtaining 





1 




-*o 


I 


a o 


«1 


a 2 


CO 

e 


*5 • 








1 . 


-*o ~ s i 






a o 


a x 


a 2 a ?j 


a 4 a 5 








. 1 




• 






\ 


\ b 2 


CO 










1 * 






\ 


\ 


\ h 


* 4 • 










1 




K 


h 


b 2 


b 3 b 4 






a o 


a i 


a 2 


a 3 




a 4 






a 5 




. a 0 


a i 


a 2 




a 3 






a 4 


«5 




\ 


K 




\ 






^3 






% 9 i 


a 0 S 2 + <Vl 


(^0^3 4" CL]$ 2 


4- a 2 


*1 


« 0 S 4+ • • 


. a 0 s 5 + . . . 




a 0 s 2 


CLq^3 "t 


a Q S 4 "t 


+ ^2 


S 2 


% s 5+ • ‘ 


• a o s e + • • • 



% 9 0 


a 0 S l + a l S 0 


UqS 2 + tqSj + 0 2 ‘S‘o 


a 0 S 3 ’ • 


. « 0 s 4 + . . . 




a 0 S 2 + a l*l 


a 0 S 3 + Cl l S 2 + a 2 ’ S l 


% 9 4 + • • 


• a 0 s 5 + • • • 


«o « 2 


a o*z + a 4 s 2 


^o ,9 4 ”t ^ 1^3 4- ei 2 s 2 


a 0*5 4 • • 


. a 0 s 6 + . . . 



and thence the final form desired. 

The question of the existence of multiple or repeated roots in an equation 
is next taken up (pp. 178-196), the main result being: The equation A = 0 
will admit of only k distinct roots of the first determinant of each of the 
last n— k bigradient arrays arising from A, and its derivative vanishes: 
and this condition being fulfilled, the equation of the said roots will be got 
by equating to 0 the determinant formed by replacing the last column of 
D k by k zeros and the 0 th , l 6 ’*, 2 nd , . . . , k fot powers of x. For example, 
A and its derivate being 

x b + x 4 - 5a ,s - x 2 + Sx + 4 , 

5x 4 + 4a: 3 - 1 5a: 2 - 2a: + 8 , 



49 



1913-14.] The Theory of Bigradients from 1859 to 1880. 



and it having been found that the first determinants of the arrays 



I (l,...,4)l 




(1 . • • • . 4), 




<1 ..... 4), 






! (5, . . . , 8) 2 




(5, . . .,8), 


1 ? 


(5 , • . . , 8) 4 


5 


(5 , . . . , 8) s 



have the values 

54, 0, 0, 0, 



the proposition states that the number of distinct roots of the equation 
A = 0 is 2, i.e. 5 — 3, and that the equation of these two roots is 



11-5-5. 

. 1 1 -5 . 

. . 5 4 1 

5 4-15 x 

5 4 -15 -2 x 2 



0 . 



As a matter of fact, this equation is 54}(x+.2)(x—l) = 0, and A=(x + 2) 2 

{x-lf. 

Lastly, Trudi takes up Sturm’s theorem for determining the number of 
roots of an equation which lie between two given values. In dealing with 
it he brings forward a new series of functions as a substitute for Sturm’s 
series, namely, 



% 




• 


> 


a 0 a Y 


«2 


% 






K 


1 




' « 0 


a l 


« 2 




\ 




X 










1 








■ \ 






X 



\ b 1 b 2 b s x 2 



Further, he points out that the individual members of this series can be 
lowered in grade by the use of his condensation-theorem, thus providing 
a variant of the series. He also notes that by means of the theorem which 
we have extended above into another condensation-theorem they can be 
transformed into 



s o 


1 A 


H ^ 

> a o 


s o 


S 1 


1 


S 1 


X 




S 1 


S 2 


X 








S 2 


h 


X 2 



and so he arrives by a different route at Joachimsthal’s series of 1854 
{Hist., ii. p. 171). 

Trudi’s work on bigradients, extending to 94 pages if both Teoria and 
Applicazioni be included, has suffered undeserved neglect. Why this 
should have been the case it is a little difficult to understand, its only 
demerits being an occasional wordiness, a not very acceptable notation, 

and a paucity of concrete examples. In his preface (p. vii) he tells us 
VOL. xxxiv. 4 



50 Proceedings of the Royal Society of Edinburgh. [Sess. 

that it was first communicated in a number of papers to the Naples 
Academy of Sciences in the year 1857. This being so, it was two years 
in advance of Zeipel’s memoir on the same subject {Hist., ii. pp. 370-372) 
and Bruno’s text- book, a fact which it is important for the reader to recall 
if any small point of similarity between two modes of treatment should 
attract attention. 



Salmon, G. (1866). 

[Lessons Introductory to the Modern Higher Algebra. 2nd ed. 
viii + 296. Dublin.] 

In a table of resultants (pp. 283-285) the final expansion of R 25 is given ? 
and the discriminant of {a, b, c, d, e \ x 4 , x s y, ... , y 4 ). 



Sardi, C. (1866) : Rajola, L. (1866) : Torelli, G. (1866). 

[Questione 47. Giornale di Mat., iv. pp. 239-240 : solution by L. Rajola, 
iv. p. 297.] 

[Teorema sui determinant a due scale, e soluzione della questione 47. 

Giornale di Mat., iv. pp. 294-296.] 

We have already seen how, from equating two forms of the resultant of 
a pair of rational integral equations, interesting identities may be obtained 
{Hist., i. p. 487 at bottom: ii. pp. 369-370, 374-375). Another instance is 
here reached, the forms of eliminant used being Sylvester’s bigradient and 
the eliminant which arises from successively substituting the roots of one 
of the equations in the non-zero member of the other equation and taking 
the product of the resulting expressions. If in connection with the latter 
we make use of Spottiswoode’s determinant expression {Hist., ii. p. Ill) 
for such a non-zero number, the identity evolved will be purely and almost 
alarmingly determinantal. 

Baltzer, R. (1864, 1870, 1875). 

[Theorie und Anwendung der Determinanten, ... 2 te Aufl. 3 te Aufl. 

4 te Aufl. Leipzig.] 

Putting (§ 11, 4 ) 

A{x) = a 0 x m + aqa?™ -1 + • • • + a m = a 0 (x - a 1 ){x - a 2 ) . . . {x - a m ) | __ 

B(a?) = b 0 x n + l x x n ~ x +••• + &„ = b 0 (x - j8 x )(aj - /3 2 ) ... {x - f3 n ) f > n 



51 



1913-14.] The Theory of Bigradients from 1859 to 1880. 

and supposing x to be one of the roots of the equation B(oj) = 0, Baltzer 
predicates the n equations 

0 = [a m - A(x)} 4 ct m -i x + 4 ■ • ■ 

0 = {a m - A(x)}x 4 + 

0 = {a m - A{x)}x 2 4 



and the m equations 



0 = b n 4 b n _ x x + b n _ 2 x 2 4 
0 = b n x 4 b n _^t? 4 

0 = b n x 2 4 



and so deduces 



a m -A(x) a m _ x a m _ 2 

a m -A(x) a m _ x 

a m - A(x) . 




= 0 , 



which must thus be the equation in A(x) whose roots are A(/8 1 ), A (/3 2 ), ..., 
A (/3 n ). Since the coefficient of the highest power of A(x) in it is 

( — 1 ) n b 0 m } it follows that 



(-])*Jg‘.A0S 1 )A08 2 )...A (p n ) = 



a m 


«m-l 


V 2 • • • • 




CL m 


a m - .... 






a .... 




K- 1 


b n . 2 .... 




b n 


b n ~ 1 .... 






b n .... 



n+m ) 



as Hesse in 1858 had shown by direct transformation. 

The bigradient form of resultant is also used (§ 11, 7) to show that when 
A and B are of the same degree 

resultant (A, B4AA) = resultant (A, B). 



A fresh proof is given of Jacobi’s theorem * that if (p be a given 
function of the (m + n — l)* ;i degree in x, it is possible to determine two 
functions u , v of the (n — l) t}l , (m — l) th degrees so as to have 



wA 4 vB = S c/>, 



* Grelle’s Journ xv. (1835) p. 108, where however m=n. 



52 



Proceedings of the Royal Society of Edinburgh. [Sess. 



where S is Sylvester s bigradient. This consists simply in taking the 
1 +n-\-m equations 



and deducing 



= 


^m+n—1 d" C m+n _ 2 X + C 


/y»2 

m+n—Z' v 


+ • • 


. . \ 


A | 


G, m + 


+ 


V 2« 2 


+ • • 




xA = 


a m x 


+ 




+ . • 




x 2 A = 






a m x 2 


+ . . 




B = 


b n + b n _ x X 


+ 


b n _ 2 x 2 


+ . . 




II . 


b n x 




b r 2 

u n- !•*' 


+ . . 





A 

xA 



^m+n — 1 ^ m+n — 2 ^ m+n — 

ci m a m _i d m _2 
• eL m et m _ i 



0. 



B 

xB 



b n - 1 

b n 



b n - 2 



+n+m 



Jacobi’s theorem of 1835 regarding Bezout’s condensed eliminant 
suggests the similar theorem regarding the bigradient eliminant,* namely, 
if w be a common root of the equations 

a 0 x m + a Y x m ~ x + • • • = 0, b Q x n + bp? 1 - 1 + • • • = 0 , 



then the signed primary minors associated with any row of 

(a 0 , , a m ) n 

are proportional to 

w m+n ~\ W m+n ~\ ... ,10, 1 . 

In dealing with the highest-common-factor of A and B and with the 
subject of elimination Baltzer profits far less than he ought to have done 
from the work of Trudi, whom indeed he does not mention. 



Isic, E. (1873): Janni, V. (1874). 

[Sul grado della risultante. Giornale di Mat., xi. p. 253.] 

[Sul grado dell’ eliminante del sistema di due equazioni. Giornale di 
Mat., xii. p. 27.] 

* Gordan (1870) in quoting the two from Baltzer says that mn of the primary minors 
of the former eliminant are secondary minors of the latter. , {Math. Annalen , iii. p. 356.) 



53 



1913-14.] The Theory of Bigradients from 1859 to 1880. 



The bigradient form of eliminant is here used in the establishing of the 
proposition that if the coefficients a r , b r , be functions of the r th degree in one 
and the same variable y, the eliminant is of the (mnf degree in the same 
variable. Janni’s proof, though not quite so good as it might have been, 
is the more interesting. The eliminant being 



a 0 a i a 2 a 3 

• (Xq a x ^3 




\ b \ ^2 5 



he, in effect, multiplies the columns in reverse order by y°, y l , y 2 , y s , y 4 
respectively, and then divides the rows in order by y 4 , y z , y 2 , y 1 , y a 
respectively, thus obtaining 



V/ 



«i2/ _1 a 2 y~ 2 a sV~ 3 
«o a \V~ X 

\ y h 

hy 2 b i y b 2 

\y 2 \y 



y 3 



In this equivalent form the elements of the first two rows are all now of 
the degree 0 in y , and those of the last three rows are all of the degree 2, 
whence comes at once the desired result. 

It should be noted that the procedure shows each term to be of the 
( mnff degree in y ; in other words, that the eliminant is homogeneous. 
Also, dispensing in the end with y, we may deduce the isobarism of the 
eliminant, its weight being mn. 



Zeuthen, H. G. (1874): Madsen, V. H. O. (1875). 

[En Bemaerking om Beviserne for Hovedsoetningen om Elimination 
mellem to algebraiske Ligninger. Tidsskrift for Math. (3), iv. 
pp. 165-171.] 

[En Bemserking om Sylvesters dialytiske Eliminationsmethode. 
Tidsskrift for Math. (3), v. pp. 144-145.] 

Zeuthen repeats Salmon’s mode of 1859 {Hist., ii. pp. 373-374) of using 
Euler’s treatment of two integral equations in x which have more than one 
common root : he is, however, more detailed, and takes the number of roots 
to be p. 



54 



Proceedings of the Royal Society of Edinburgh. [Sess. 



Lemonnier, H. (1875, 1878). 

[Theoremes concernant les equations qui ont des racines communes. 
Comptes-Rendus .... Acad, des Sci. (Paris), lxxx. pp. 111-112, 
252-255.] 

[Memoire sur 1’elimination. Annates de Vlfcole Norm. Sup. (2), vii. 
pp. 77-96, 151-214.] 

Lemonnier’s condition for the equations 



%x m + ■ • • + a m = 0, b 0 x n + ••• + &„ = 0 

having k common roots is different from Trudi’s, but fortunately for com- 
parison is very easily expressed in Trudi’s notation. It is * that the first 
k determinants of 



: K> ' ' 


• 5 ®m)n—k + 1 


1 (&<)>•• 





shall vanish, and the first determinant of 



(“o. • • 


• ? ®>m)n—k 




• j l*n)m—k 



shall not vanish. The former part of the condition recalls Zeipel’s of 1859 : 
the latter is an important necessary adjunct. When, however, the equation 
of the common roots 

\(x k , a* -1 , . . . , a? 0 ) = 0 



{ a Q > • • 


• 5 a m)n-k j 




• j bfim-k 1 



happens to be given along with the condition, it is less necessary to mention 
the latter part, as the determinant involved is the coefficient of x k in the 
said equation. 



Muir, T. (1876). 

[New general formulae for the transformation of infinite series into 
continued fractions. Trails. Roy. Soc. Edin., xxvii. pp. 467-471.] 

[On the transformation of Gauss’ hypergeometric series into a continued 
fraction. Proc. London Math. Soc., vii. 112-118.] 

The fundamental theorem, which is established in two different ways, 
is not essentially different from Heilermann’s of 1845 (Hist., ii. p. 361). 
The second of the two ways is the more interesting. Beginning with the 
series 

a 0 + ape + ap? + ap? + ••••, or / 0 , 
b 0 + bp + bp? + bp 3 + ••••, or fi , 

* This is in accordance with the statement in § 13 of the complete memoir, and is 
somewhat different from that first published. 



55 



1913-14.] The Theory of Bigradients from 1859 to 1880. 



and subtracting b 0 times the first from a 0 times the second, and dividing 
the result by x, we obtain 



a 0 


a i I 


+ 


a 0 ^2 


X + 


I a o a s 


\ 






b Q ^2 




1 b 0 b 3 



or / 2 say ; 



and by subtracting | ajb x | times the second from b 0 times this third series 
and dividing by x there results 



a o a Y 

■ \ 


« 2 

\ 


+ 


tt 0 CLy 

• \ \ 


x + 


CIiq CL-^ CL 4 

• ^1 ^3 


%? + • • • , or / 8 say ; 








\ ^1 ^3 




\ \ h 4, 





and so on. The outcome is 

a 0 4- a x x + a 2 x 2 + • • • • 6 1 q ^ 

b 0 + bjX + b 2 x 2 + • • • 0 o - -j- _ O 3 P q^q^ x 

1 °2 ~ -q— - 

C7 3 



where 0 O , 6 V 0 2 , • • • • are the first terms of f 0 , f v f 2 . . . respectively. 



Yent^jols, . (1877). 

[Sur un probleme comprenant la theorie de l’elimination. Gomptes- 
Rendus . . . Acad, des Sci. (Paris), lxxxiv. pp. 546-549.] 

Ventdjols’ subject would have been much better described by Lemonnier’s 
title of 1875. In substance nothing fresh is brought forward. 



Dickson, J. D. H. (1877). 

[A class of determinants. Trans. Roy. 80c. Edin ., xxviii. pp. 625-631.] 
[The numerical calculation of a class of determinants, and a continued 
fraction. Proc. London Math. Soc., x. pp. 226-228.] 

The determinants here considered are the bigradients dealt with by 
Heilermann (1845) and Muir (1876). They also arise in the same connection. 

Mansion, P. (1878). 

[Sur l’elimination. Bulletin . . . Acad . . . . de Belgique, xlvi. pp. 899— 
903.] 

What is interesting here is Mansion’s mode of obtaining the evanescent 
bigradient array that results from the existence of common roots. The 
equations being 

A(aj) = a 0 cc 5 + ... +a 5 = 0, B(x) =* + . . . + & 4 = 0 



56 



Proceedings of the Royal Society of Edinburgh. [Sess. 



and the common roots a, /3, y, it follows that 



a m a n A (a) 




a m a” aA(a) 




a m a n B(a) 




a m a n aB(a) 




a m a n a 2 B(a) 


p m p* AOS) 




/3~ 0* pm 




/T /3 n B (P) 




/3 m / 3 n (3B((3) 




/ 3 m (3 n /3 2 B(/3) 


T 7“ A(y) 


5 


7” 7" yMy) 


5 


7“ 7“ b <7> 




i m T 7 B(y) 


5 


T y n 7 2 B(y) 



are all equal to 0 ; so that, if we temporarily write 



(m , n , p) for the alternant | a m /3 n y p | , 

we have 

(mn5)a 0 + (mni)^ + (mn?>)a. 2 + (mn2)a s + (mn\)a b + (mnO)a b — 0 

(mw6)a 0 + (innbya-^ + (mni)a 2 + ( mn3)a s + (mn2)a 4 + (mnl)a 5 = 0 

(mn4:)b 0 + (mu 3)b 1 + (mn2)b 2 + (mnl)b^ + (mn0)b 4 = 0 
(mn5)b 0 + (mni)b l + ( mn3)b. 2 + ( mn2)b 3 + (mn\)b 4 = 0 

(mn6)b 0 + (mn5)b 1 + (mni)b 2 + (mn3)b s + (mn2)b 4 = 0. 



Here, however, by taking any two of the numbers 0, 1, 2, 3, 4, 5, 6 as 
values for m, n two of the alternants will disappear, and we shall be able 
to eliminate the five others, the final and complete result thus being in 
Cayley’s notation 





% 




a 2 


00 


a l 


a b 


a o 


a i 




a B 


a 4 


“5 








\ 


h 


b 2 














h 


*4 




h 






h 


h 







For example, putting m, n equal to 0, 1, then equal to 0, 2, and finally 
equal to 1, 2, we should have the particular three results which in accord- 
ance with our usage under Trudi we might write 



(a 0 , . . 


■ 


(*„ ■ • 


• ■ > ^t)s ! 



All this, however, is considerably modified from Mansion’s exposition. 



Gunther, S. (1879). 

[Eine Relation zwischen Potenzen und Determinanten. Zeitschrift f. 
Math. u. Phys., xxiv. pp. 244-248.] 

The subject here is simply the evaluation of the bigradient which is the 
discriminant of (x m+2 — l)/(x— 1), the result being 

(m + 2 ) m . 

For example, when m is 2, 

1111 . 

. 1111 
12 3 .. 

. 12 3 . 

. 1 2 3 



4 2 . 



57 



1913-14.] The Theory of Bigradients from 1859 to 18.80. 

Gunther’s proof is unnecessarily lengthy. The determinant can be readily 
transformed into one whose diagonal has for its elements 1 repeated m + 1 
times and m + 2 repeated m times, and whose other terms all vanish. For 
example, when m is 2, the requisite operations are 

row 5 - row 4 + row 2 , 
row 4 - row 3 + row 4 , 
row 3 — row 2 — rowq . 

Mansion, P. (1879). 

[On the equality of Sylvester’s and Cauchy’s eliminants. Messenger of 
Math., ix. pp. 60-63.] 

Mansion’s proof is not essentially different from the process of applying 
Trudi’s condensation-theorem to Sylvester’s bigradient. The additional 
fact, to which Mansion draws attention, namely, that many minors of the 
one eliminant have equivalents among the minors of the other, is also 
virtually included in Trudi. Thus, the four identities which Mansion 
indicates in the form (see his fig. 11) 

(Zq cq a 2 a B a 4 cl^ a,^ . 



G t>2 b B 

where the X’s, /Ps, Ps stand for 

&i a 0 b 2 + a 1 b 1 af) B + a l b 2 + afb 4 af> B + a 2 b 2 + « 3 & 4 - a 4 b 0 a 2 b s + a B b 2 - a b b 0 a B b B - 

b 2 a 0 b B + af) 2 a Y b B + a 2 b 2 a 2 b B + a B b 2 + a,b 0 a B b. 3 - a 6 b 0 + a 4 b 2 a b h x a 4 b B - a Q b l 

h a A a A a A ~ a 6 h o a A - a A a A~ a 6 b 2 

are only four of the ten noted by Trudi, the others being excluded, so to 
speak, by drawing three vertical dotted lines on the right of each determi- 



*0 


a l 


a 2 


« 3 


a 4 


a b 


% 




a o 


a i 


a 2 


a 3 


a 4 


ft 










\ 














\ 


\ ■ 


h 






\ 




\ 








K 


h 




CO 






\ 




h 


h 









■ 




b 2 


b 0 b x 




b 3 


\ b i b 2 






CO 

oq 

*< 


K 




P i H H 




ft 


V 1 v 2 v 3 


V 4 


V 5 



ne 

/*e 



58 Proceedings of the Royal Society of Edinburgh. [Sess. 

nant instead of continuing the horizontal dotted lines all the way towards 
the right. 



From the foregoing there is probably no serious omission of papers 
dealing directly with bigradients and in particular with the bigradient 
eliminant. But, as it is possible to study the subject of the common roots 
of two intregral equations without direct reference to bigradients, and as 
the other determinants that may then be used can generally be transformed 
into bigradients, it will doubtless be of service to the student of determinants 
to give the following list of titles of papers on elimination. When taken 
together with the preceding papers on the same subject they will also be 
helpful to the student of the theory of equations : — 

1870. Gordan, P. Ueber die Bildung der Resultante zweier Gleichungen. 

Math . Annalen, iii. pp. 355-414. 

187 2. Naegelsbach, H. Ueber die Resultante zweier ganzen Functionen. 

Zeitschrift f. Math. u. Phys., xvii. pp. 333-346. 

1876. Darboux, G. Sur la theorie de lelimination entre deux equations 

a une variable. Bull, des Sci. Math., x. pp. 56-64 : (2) i. pp. 

54-64. 

1877. Rouche, E. Sur l’elimination. Nouv. Annates de Math. (2), xvi. 

pp. 105-113. 

1877. Igel, B. Einige Satze und Beweise zur Theorie der Resultante. 

Sitzungsb. . . . Akad. d. TFiss. (Wien), lxxvi. pp. 145-168. 

1877. Forestier, C. Exposition succincte de quelques methodes d’elimi- 

nation entre deux equations. Mem. de V Acad, des Sci. 

(Toulouse) (7), ix. pp. 142-163. 

1879. Biehler, C. Sur la theorie des equations. Dissert. 60 pp. 

Paris. 

1879. Falk, M. Sur la methode de l’elimination de Bezout et Cauchy. 

Nova Acta Reg. Soc. (Upsala), x. No. 15, 36 pp. 

1879. Hioux, V. Note sur la methode d’elimination Bezout-Cauchy. 

Nouv. Annates de Math. (2) xviii. pp. 289-295. 

1879. Mansion, P. Sur l’elimination. Bull. . . . Acad. . . . Belgique 

(2), xlvi. pp. 899-903: xlvii. pp. 532-541: xlviii. pp. 463-472, 

473-490, 491-526. 

The papers of Falk and Manson devote some little space to reviewing 
the work of their predecessors, and are therefore additionally helpful. They 
do not, however, mention Trudi, nor indeed does any one of the other 
writers of the period. 



59 



1913-14.] The Theory of Bigradients from 1859 to 1880. 

It may be noted as a significant fact in connection with the history 
of the subject that in 1876 the editors of the Nonvelles Annates found 
themselves called on to republish Cauchy’s important paper of 1840 (see 
Hist., i. pp. 240-243). Its reprint occupies pp. 385-416, 433-451 of vol. xv. 
of the second series. On this account, save for junior readers, the 
“ exposition succincte ” above noted was quite unnecessary. 



LIST OF AUTHORS 



whose 

1859. Bruno, F. Faa di . 

1862. Trudi, N. 

1866. Salmon, G. 

1866. Sardi, C., etc. . 

1864- Baltzer, R. . 

1870. Baltzer, R. . 

1875. Baltzer, R. . 

1873. Isis, E. . 

1874. Janni, V. 

1874. Zeuthen, H. G. 



ritings are herein dealt with. 


32 


1875. Madsen, V. H. O. 


33 


1875. Lemonnier, H. 


50 


1878. Lemonnier, H. 


50 


1876. Muir, T. . 


50 


1877. Ventejols 


50 


1877. Dickson, J. D. H. 


50 


1878. Mansion, P. . 


52 


1879. Gunther, S. . 


52 


1879. Mansion, P. . 


53 ! 





53 

54 
54 

54 

55 
55 

55 

56 

57 



{Issued separately February 19, 1914.) 



60 



Proceedings of the Royal Society of Edinburgh. [Sess. 



VI. — The Kinetic Energy of Viscous Flow through a Circular 
Tube. By Professor A. H. Gibson, D.Sc., University College, 
Dundee. 



(MS. received October 11, 1913. Read December 15, 1913.) 



In the stream-line flow of a viscous fluid through a circular pipe of radius 
a, the velocity of flow at any radius x is given by 



where 



v = k(a 2 - x 2 ), 

k=— . . 

4 fx dl 



From this it follows that the kinetic energy of the moving column per 
unit volume is given by 



— I 27rxv 3 dx 
2gJo 



I — . 2t rife* [ a {aPx 
2 g Jo 



- 3 cfix 3 + 3 a 2 x b - x 7 )dx 



w 



2 9 



Jtt Wa 8 . 



( 1 ) 



The mean velocity v of flow through such a tube is given by 

v = J ka 2 , 

so that the apparent kinetic energy, or the product of the mass flow and 
one-half the square of its mean velocity, is 

— • ira 2 [^ka 2 f 
2 Q 

= “ • (2) 

The true kinetic energy is therefore twice that calculated as in (2) 
from the mean velocity. 

In the majority of experiments carried out to determine the co- 
efficient of viscosity of a fluid, the head necessary to maintain a 
measured velocity of flow through a tube of known diameter and length 



1913-14.] Viscous Flow through a Circular Tube. 



61 



is measured, and the coefficient //. is then determined from Poiseuille’s 
equation, 

h = ^ (3) 

Where h is measured by the difference of pressures at piezometer 
orifices at two points in the wall of the tube, this equation is rigorously 
true. Where, however, as is more often the case, the upper end of the 
tube projects into a reservoir of the fluid, while its lower end discharges 
freely, the head being measured from the free surface in the reservoir 
to the centre of the discharging end of the tube, the true equation 
becomes 

h — 32/^ _j_ k.E. of discharge + head loss at entrance to tube. . (4) 

The two last terms become decreasingly important as the length of the 
tube increases, but, with a fairly short tube, account for a very appreciable 
portion of the whole head. In many cases in which the details of viscosity 
experiments have been published, the kinetic energy of discharge has been 
calculated erroneously from the mean velocity as in formula (2), while 

various allowances, varying from zero to have been made for the head 

9 

loss at entrance to the tube. In a thin- walled tube projecting into a 
reservoir, the loss at entrance, with an inviscid fluid, may readily be shown 

to be equal to while the effect of viscosity is to reduce this loss some- 
what. As the walls of the tube become thicker the conditions approximate 
more nearly to that of a tube whose end opens flush with the sides of the 
reservoir, in which case, in large tubes conveying water, the loss is 

approximately ‘5^-. The true value of this loss for any actual projecting 

Zg 

tube may therefore be expected to be given by c^- , where c increases with 

^9 

the relative thickness of the walls, and, for such a fluid as water, has a 
value somewhere between - 5 and kO. 

The following experiments have been carried out with a view of 
checking the accuracy of the deductions leading to formula (1), and 
of determining the value of c for tubes of small bore. In each case 
the tube used projected for some distance into the upper reservoir 
and discharged freely at its lower end. The head from the free 
surface in the reservoir to the centre of the outlet was measured, and 
the discharge was collected and measured. The fluid was water, 



62 Proceedings of the Royal Society of Edinburgh. [Sess. 

and the purely viscous loss was calculated from Poiseuille’s value 
of ju, viz., 

•0000181 

^ 1 + -03368* + -00022 W 

Three tubes were used, of the following dimensions : — 



Tube. 


Diameter in cm. 


Length. 

Cm. 


Ratio 

external 


Internal . 


External. 


internal 
diameter =m. 


A 


*0715 


•1073 


4-29 


1*50 


B 


*1470 


*1960 


6-66 


1*33 


C 


*2580 


•9000 


38*20 


3*50 



For tubes A and 13, £=14-2° C., making [x= *0000119. 

For tube C, £=12*9°C., „ /* = *0000123. 

Since the pressure in the interior of the jet at the point of discharge 

T 

is greater than atmospheric by an amount — , where T is the surface tension 

and r the radius of the jet, the effective head is less by this amount than 
the measured head. 



Thus, for tube A, T = *073 grms. per cm. ; — = 2*028 cm. 

r 

„ B, T = '073 „ ; 1 = 1-00 „ 

r 

„ C, T = -075 „ ; 1=0-57 „ 

r 

This correction is applied in the following tables, which give the 
experimental results. 



Tube A. 







Loss of head in cm. 






v 2 




Experiment. 


Total. 


In viscous 
resistance. 


Due to T 
at outlet. 


Residue 

(-*©■ 


V 

c. per sec. 




L 


1 


16-50 


12-400 


2-028 


2-072 


39-00 


•775 


2-68 


2 


16-22 


12-200 


55 


2-002 


38*40 


*750 


2-68 


3 


8-48 


5*980 


55 


0-475 


18*82 


*1805 


2-63 


4 


8*35 


5*870 


55 


0*452 


18-48 


•1740 
Mean = 


2-60 

2-65 



1913-14.] Viscous Flow through a Circular Tube. 



63 



Tube B. 







Loss of head in cm. 










Experiment. 


Total. 


In viscous 
resistance. 


Due to T 
at outlet. 


Besidue 

K> 


V 

c. per sec. 


v 2 

w 


1c. 


1 


16-02 


8-155 


1-000 


6-865 


69-60 


2-470 


2-78 


2 


16-64 


8-390 


55 


7-250 


71-30 


2-595 


2-80 


3 


12-56 


6-905 


55 


4655 


58-75 


1-760 


2-65 


4 


11-81 


6-550 


55 


4-260 


55*70 


1-581 


2-69 


5 


7-50 


4-501 


55 


1-999 


38-23 


0-745 


2-68 


6 


7-46 


4-490 


55 


1-970 


38-20 


0-744 
Mean = 


2-65 

2-71 



Tube C. 



1 


16-90 


11-98 


0-57 


4-35 


57-90 


1-705 


2-55 


2 


16-60 


11-85 


55 


4-18 


56-90 


1-646 


2-54 


3 


12-43 


9-30 


55 


2-56 


44-65 


1-015 


2-53 


4 


12-55 


936 


55 


2*62 


44-95 


1-029 


2-54 














Mean = 


2-54 



From these results it appears that the sum of the residual losses is 
between 2*5 and 3*0 times — . Of this, the kinetic energy of discharge 

accounts for 2~. The remainder, incurred at entry to the tube, is equal 

* 9 

to Ctz- , where c has mean values as follow : — 

2g 



Ratio 

outer diameter 


1-33 


1-50 


3-50 


inner 

(=m) 


Mean value of c 


•71 


•65 


•54 


1 








2 - V 


•70 


•64 


•52 


m 2 









The value of c appears to increase slightly with an increase in speed. 
Its mean values over the range of values of m occurring in the experi- 
ments are given with fair accuracy by the relationship 




and as this also satisfies the two extreme conditions, i.e. makes c = 1 when 
m=l, as in a thin- walled tube, and makes c — m 5 when m is very large, 
values calculated by this relationship are probably fairly accurate for all 
intermediate values of m. 



(. Issued separately February 19, 1914.) 



64 



Proceedings of the Royal Society of Edinburgh. [Sess. 



VII. — The Axial Inclination of Curves of Thermoelectric Force : a 
Case from the Thermoelectrics of Strained Wires. By John 
M‘Whan, M.A., Ph.D., Lecturer in Mathematics in the University of 
Glasgow. Communicated by Professor Andrew Gray, LL.D., F.R.S. 

(MS. received October 17, 1913. Read February 16, 1914.) 

In a communication to the Royal Society of Edinburgh,* Mr J. D. Hamil- 
ton Dickson has examined with great care the valuable results of Professors 
Dewar and Fleming on the thermoelectromotive forces of various couples, 
and has come to the conclusion that the curve representing the thermo- 
E.M.F. is in every case a parabola whose axis is, not vertical as had always 
been assumed, but inclined a definite though very small angle to the 
E.M.F.-axis. 

This remarkable result has led me to go back to some experiments 
which I made a few years ago on the thermoelectric properties of longitu- 
dinally strained metal wires, to see if by any chance the same phenomenon 
might be detected there, and in one instance (only) I have been able to 
establish its existence unmistakably. The experiments in question, which 
I have described elsewhere, j* were made on couples consisting each entirely 
of one and the same pure metal ; but one wire of the couple might be subjected 
to any desired longitudinal tension while the other remained unstrained. 
The temperatures of the junctions were the same in all the experiments, 
one junction being steam-heated, the other water-cooled. 

On reference to the curves showing the relation of the tension in the 
strained wire to the thermo-E.M.F. of the couple, only one was found to be of 
parabolic shape, namely, that for nickel. The E.M.F.’s in non-magnetic 
metals nearly all obey a straight-line law up to the point where overstrain 
sets in : the only other magnetic metal tested, bismuth, gave no simple 
relation between E.M.F. and strain. A closer examination of the nickel- 
curve showed that, while it afforded good grounds for suspecting an in- 
clination of the axis, the observations had been neither numerous enough 
nor of the high order of accuracy necessary for certainty, and it was 
accordingly decided to repeat the experiment. This repetition proved 
extremely laborious, and only after some five or six attempts (each necessitat- 

* Trans. R.8.E . , xlvii. 737-791, 1910-11. 
t Diss., Gottingen, 1911. 



65 



1913-14.] Inclination of Curves of Thermoelectric Force. 

ing the mounting of a fresh and freshly annealed wire) was the accompanying 
curve, the figures for which appear in Table I., obtained, in which only one 
of the thirty plotted points lies appreciably wide. 



Table I.— Table showing Loads carried by Strained Wire (Mean Diameter 
0-682 mm.) and Corresponding E.M.F.’s, reduced to Mean Temperature- 
Range of 75° C. June 4, 1913. 

Load (kg.) . 

E.M.F. (volt x 10 6 ) 



0 

0-600 


0-5 

2-101 


1 

3-459 


1-5 

4-732 


2 

5-932 


2-5 

7T20 


3 

8-261 


3-5 

9-318 


4 

10-300 


4-5 

11-289 


5 

12T41 


5 5 

12-920 


6 

13-718 


6-5 

14-471 


7 

15-092 


7-5 

15-649 


8 

16-101 


8-5 

16-299 


9 

16-833 


Q-F, 

17-080 


10 

17*211 


10-5 

17330 


11 

17-363 


11-5 

17-302 


12 

17-178 


12-5 

16-970 


13 

16-661 


13-5 

16-272 


14 

15-800 


14-5 

15-260 



It may be remarked, with reference to this curve and the table of values, 
that the loads given as abscissae do not include the weight (175 gm.) of 
the weight-pan. This accounts largely, though not entirely, for the fact 
that “zero” load on the curve shows an E.M.F. of 0-60 xlO -6 volt; the 
unavoidable manipulation of the annealed wire in mounting it (and 
consequent slight strain) gave rise to an observed E.M.F. at (true) zero 
load of about 0*066 X 10 -6 volt, which accounts for the remainder of 
the discrepancy. During the experiment — which lasted some eight con- 
secutive hours — it was, of course, impossible to secure that the temperatures 
inside the steam jacket and cold-water jacket which surrounded the 
two junctions of the couple should remain constant. Besides the unavoid- 
able small variations due to the replenishment of the boiler and other 
incidental parts of the experiment, there comes into play a very con- 
siderable thermoelastic cooling effect* at the junctions as the load is 
increased. Thus, though these junction-temperatures, which were read 
between every two galvanometer readings, proved fairly steady in the 
neighbourhood of 97° C. and 21° C. respectively, varying at most by about 
half a degree, for greater accuracy all the observations of E.M.F. used in 
plotting the curve were reduced by interpolation to a mean temperature- 
difference of 75° C. The reduction was easily performed from a series of 
temperature-E.M.F. curves for different constant loads, prepared in connec- 
tion with the original experiments. 

Examination of the Curve . — The curve, when drawn to a large scale 

* Loc. cit ., pp. 36-43. 



VOL. XXXIV. 



5 



66 



Proceedings of the Royal Society of Edinburgh. [Sess. 




LOAD 



67 



1913 - 14 .] Inclination of Curves of Thermoelectric Force. 

(1 inch = 05 kg. for abscissae, = 10~ 6 volt for ordinates), was examined to 
determine (i.) if it was a parabola, and (ii.) if so, if its axis was vertical or 
inclined. The method of examination differed from that employed by 
Dickson, in that it was first tacitly assumed that the curve was a parabola, 
the fact that the midpoints of several parallel chords were found to lie on 
one straight line giving support to this assumption, while not completely 
justifying it. The straight line in question then gave the direction of the 
axis. To determine the vertex of the curve, the tangent to it at right 
angles to the axial direction was drawn : this is easily performed with 
considerable accuracy by the aid of a long slip of glass having one straight 
line ruled on it all its length, and a shorter one at right angles across the 
slip. The shorter one is made to cover the determined axial direction, and 
then slid along it until the longer one just touches the curve. (The glass 
is, of course, turned with the lines next the paper.) The axis was then 
drawn at right angles to the tangent at the vertex, and the focus determined 
by trial, again with the glass slip, by finding the point on the axis whose 
distance from the vertex was half its perpendicular distance from the curve. 
This determined the latus rectum. Lastly, the inclination of the curve- 
axis to the E.M.F.-axis was measured roughly by protractor and (much 
more accurately) by square-counting, to find its tangent. The results of 
these various measurements were : 

Co-ordinates of vertex . . (22*48", 17*34") 

Length of latus rectum .... 25*2" 

Axial inclination, 

(i.) by protractor (mean of 8 readings) . 3° 54' (about) 

g 

(ii.) by square-counting (tan o> = Y^g) . 3° 48' 

From these data it is now possible to calculate the equation of the parabola, 
and the final stage of the work is then the verification that the values 
given in Table I. satisfy this equation to a sufficient degree of accuracy. 
The equation, as calculated to seven significant figures for each coefficient, 
was 

9956077a? 2 - 1322564 xy + 43922 if - 407990900* + 279653900 y - 206538300 = 0. 

For any assigned value of x the equation gives two values of y, one of which, 
since the coefficient of y 2 is very small compared with the other coefficients, 
will be practically infinite (and negative). Neglecting these infinite solu- 
tions as foreign to the problem, Table II. gives a comparison of the E.M.F.’s 

(y) corresponding to various loads f~) as calculated from this equation. 



68 



Proceedings of the Royal Society of Edinburgh. [Sess. 

and the E.M.F.’s actually observed at the same loads. The agreement is at 
once sufficiently obvious : from the arrangement of the signs in the column 



Table II. 



Load (kg.). 


Calculated value 
of E.M.F. 

(Volt) 


Observed value 
of E.M.F. 

< 10 6 ). 


Difference. 


0 


0-641 


0-600 


+ 0-041 


1 


3-547 


3-459 


+ 0-088 


2-5 


7-307 


7-120 


+ 0-187 


4 


10-511 


10-300 


+ 0-211 


5 


12-326 


12-141 


+ 0-185 


6 


13-877 


13-718 


+ 0-159 


7*5 


15-685 


15-649 


+ 0-036 


9 


16-855 


16-833 


+ 0-022 


10 


17-262 


17-211 


+ 0-051 


11 


17-362 


17-363 


- o-ooi 


12-5 


16-915 


16-970 


- 0-055 


14-5 


15-148 


15-260 


-0-112 



of differences it seems probable that the determination of the axial in- 
clination has been slightly at fault (rather too large), and that a more 
accurate determination would make the agreement still more striking. 
As it is, the initial assumption that the curve is a parabola appears sufficiently 
justified. 



{Issued separately March 20, 1914.) 



1913-14.] Path of Ray of Light in Rotating Solid. 



69 



VIII. — The Path of a Ray of Light in a Rotating Homogeneous 
and Isotropic Solid. By E. M. Anderson, M.A., B.Sc. Com- 
municated by The General Secretary. 

(MS. received November 3, 1913. Read January 19, 1914.) 

The path of a ray of light in irrotationally moving media was first 
investigated mathematically by Fresnel, who showed that to account for 
the observed phenomena it is necessary to suppose that, the aether being 

fixed, the medium imparts - — — of the amount of its own motion, resolved 

in the line of the refracted ray, to the advancing disturbance. This 
conclusion is also a necessary consequence of the modern Theory of 
Relativity, which, while holding that, with reference to axes with regard 
to which the medium is stationary at any point, the speed of light depends 
only on the refractive index, for any other system leads to the above result. 

Using this formula, it is possible to calculate the path of a ray of light 
in a rotating homogeneous and isotropic solid, when the velocity produced 
by rotation is small compared to that of light itself. We shall first 
consider the case of a body rotating about an axis fixed in space, and at 




right angles to the line joining two points A and B, through which we 
will suppose the path to pass. If r be the distance of the disturbance 
at any moment from this axis, and cp the angle made by the ray with 
the direction of r produced ; if further co be the velocity of rotation, and 
c the speed of light ; then the total velocity of the ray is 

c wr sin 4> (/jl 2 - 1) 



70 



Proceedings of the Koyal Society of Edinburgh. [Sess. 



or 

where 



D = 



D + Er sin <f > , 
and E = o>— 



[X /x- 

Then the condition for a brachistochrone is first evidently that the- 
path shall lie entirely in the plane of rotation, and further 

8 f — =0, 

J D + E?’ sin (j> 

or, neglecting the second order of small quantities 



\ f ds j, f i 



dsEjr sin <f> 



= 0 . 



If we consider the part of the brachistochrone intercepted between 
A and B, then Jcfe is the total length of the curve AB, while Jds r sin 0 
is twice the area traced out by the radius vector. 

It is easy to see that, while an increase of the length of the path leads 
to an increase in the time taken, an increase in the area covered by the 
radius vector will have the opposite effect, if area be reckoned positive 
when swept out in the direction in which the solid is rotating. The last 
equation may be interpreted to mean that for any slight deviation from 
a brachistochrone these two causes of variation must exactly balance, and 
that they will do so if an increase in length is accompanied by D/2E times 
the same increase in area. Substituting we find 

D fxc 
2E == 2o i (^-l)' 

It is easy to show that a curved path, with a certain radius of curvature, 




constant within the limits already assigned, will satisfy the above condition. 
In the first place, it is a well-known theorem, and may be proved by the 



71 



1913 - 14 .] Path of Ray of Light in Rotating Solid. 

calculus of variations, that for any given length of line joining two points 
A and B (fig. 2), that form of curve which subtends a maximum area with a 
third point O in the same plane is an arc of a circle. We shall not, however, 
use this result, but another which follows from it, or may be regarded as 
the last step in its demonstration, namely, that if AFDGB be the circular 
arc of required length, and ACDEB a slight variation from it having 
exactly the same length, then the areas 0 ACDEB and 0 AFDGB are 
equal to the first order of small quantities. 

If now (fig. 3) we consider ALB as a possible circular path for light 
in the rotating solid, and let APB be any slight deviation from it, in the 
same plane, but not necessarily of the same length as ALB ; then if the 
lengths of the two curves be not the same, let AMB be the circular 




arc joining A and B which has the same length as APB. Then by the 
theorem just stated AMB and APB subtend the same area at any point in 
their plane to the first order of small quantities. Thus the time taken by 
an ethereal disturbance to traverse the paths AMB and APB will be equal 
with the same degree of accuracy. 

Let us next consider the difference of length, and of area subtended by 
the two circular arcs ALB and AMB. Let R be the centre of the chord 
AB, and C and D the respective centres of the two circles. If then 

Ah = a 

AT) = p 

AC = p + e, 

then the area enclosed by the two arcs is 



72 



Proceedings of the Royal Society of Edinburgh. [Sess. 



which equals 



2e( p sin _1 — 

V P Jo 2 - aV 



P Jp 2 - a 2 ' 

The difference in length of the two arcs is 





the former result divided by p, where p is the radius of curvature. 

Thus the area enclosed between two nearly coincident circular arcs, 
ending at the same points, is p times their difference of length. Also, from 
what we have already seen, the difference in the area subtended at any 
point in its plane by a circular arc and any slight deviation from it will 
be p times the difference in length of the two curves. This assumes that 
the point of subtension is so situated that the area swept out by the radius 
vector is wholly positive or wholly negative. Obviously, for a point on 
the concave side the difference of area will be of the same sign as the 
difference in length, while for a point on the convex side the sign will be 
opposite. 

Now, we have seen that the condition for a brachistochrone in the case 
we are considering is that an increase of length in the curve between any 
two points shall be accompanied by an increase of area subtended at the 



centre of rotation of times the amount, area being counted 

2co( J u 2 — 1) 6 

positive when traced out in the same direction as the body is rotating. 
This condition is obviously satisfied by a circular arc whose radius of 
curvature 



c p, 

W 2(p? - 1) 

and which is concave or convex to the centre of rotation according as the 
wave motion with regard to that centre is in the same or in the opposite 
direction to the rotation. 

We will next consider the case where the medium, in addition to its 
rotatory motion, has an uniform translatory motion v, as before, small com- 
pared to the velocity of light. If 6 be the angle between the direction 
of the ray and that of v, the total velocity is 

c <or sin <jf>(/x 2 - 1) fcos0(/x 2 -l) 

~ + ^2 + ^2 ’ 



where 



D + Er sin </> + F cos 0 , 
tr _ v ( A*- 2 ~ 1 ) 



73 



1913-14.] Path of Ray of Light in Rotating Solid. 



The condition for a brachistochrone is 

ds 

D + E?' sin $ + F cos 0 
or to the first order of small quantities 






= 0 



fs-‘j 



dsFr sin <£ dsF cos 0 



D 2 



D 2 



= 0 . 



Now, as the projection of the path AB on a line drawn parallel to v 
is a constant, the last term vanishes, and we therefore arrive at our 
previous result. 

In both this and the previous case the curves calculated are those 
followed in space with regard to the assumed axes of no velocity. The 
paths traced out in the solid itself can be deduced as follows. It is easy 
to show that a ray which penetrates the rotating body in a straight line, 

with velocity - , will leave a trace in the solid of curvature } which will 
fk c 

he convex to the centre of rotation if the ray be moving with regard 

to the centre in the direction of rotation. The actual curvature of the 

o / 2 1 \ 

path of light is — — in the opposite direction. By subtraction we 

Cfk 



get — as the curvature of the path traced out in the solid ; the radius of 

Cfk 



curvature is ~ , and the curve will be convex or concave to the centre 
2oo 

of rotation according as the radius vector of the disturbance moves along 
with or against the rotation. This result will apply to both the cases 
so far considered. 

We have next to deal with the case in which the path of the ray is not in 
the plane of rotation. Let us consider what path will be followed between 




two points A and B in a medium rotating about an axis LM (fig. 4). Let 
P be the plane passing through A and perpendicular to LM ; 0 the point 



74 



Proceedings of the Royal Society of Edinburgh. [Sess. 



of intersection of that axis; C the projection of B on P. Join CA and AB, 
and let \fs 0 be the angle CAB. Let ADB be a possible path for light 
between A and B, and let AEC be its orthogonal projection on P. Let 
\]s be the angle between any element of the curve and the corresponding 
element of the projection; r the distance of the latter element from the 
point O, and (p the angle it makes with the direction of r produced. Then 
the speed of light at any point on ADB is 



c • , , fX 2 - 1 

- + cor sin <jt> cos if/ ™ - , 

/x ^ 

or 

D + Er sin <£ cos if/ , 

where D and E have the same meanings as before. The condition for a 
brachistochrone is therefore 



v fds s f 

‘ h- s ) 



Er sin cos i J/ds 
IP 



If now ds' be the element of the projection corresponding to any element 
ds, ds ' = ds cos \fs, and our condition may be written 



s fds « fEr sin d>ds A 

s Jd- s ]—w - =0 



Let Q be the cylindrical surface whose generators are parallel to LM, 
and which passes through the curve ADB and its projection. Then it is 
evident that for any curve on Q joining A and B the latter half of the 
expression vanishes. Hence the curve of this class which most nearly 
satisfies the brachistochrone condition is the shortest in length, or otherwise 
the curve for which \{s is constant. 

We may therefore confine ourselves to curves for which this condition 
is fulfilled. Denoting the length of the arc AEC by l, and that of CB by a, 

tan ^ = T’ and C0S ^ = -Jiha?’ 

The condition may therefore be written 



As 



fds' _ 

JT~ 



1, we get 



g fds Jl 2 + a 2 _ « f Er sin <pds' _ ~ 

J D^ J W 



Ihl ^ f E?’ sin <pds _ n 



or in other words, being the rectilineal angle CAB, the increase of area 
subtended at O by the curve AEC must be ^ C ^- r ^ Q times its increase of 
length, to the first order of small quantities. From this it follows that 



75 



1913-14.] Path of Ray of Light in Rotating Solid. 



the radius of curvature of the projected curve is f CQS V'oM > The curve 

^ J 2o)( m 2 -1) 

itself follows from this condition and the fact that \Js is constant. 
Within the limits considered it is part of a circular helix. Its radius of 



curvature is / L— in a direction perpendicular to the axis of 

2o> cos yfr 0 (nA 2 — 1) 

rotation. This conclusion holds good whether or not we consider our 
rotating body to have also a translatory motion with regard to the axes 
of reference. 



Note on Mr Anderson’s Paper. By Sir Joseph Larmor, 

M.P., F.R.S. 



Mr E. M. Anderson’s elegant argument may be paraphrased as 
follows : — 

Let v he any coplanar velocity of the medium, and set E = v(/ul 2 — 1)/m 2 
and D = c/iul; then the time of passage of a ray restricted to any artificial 
path is 

f— — , approximately J- f ds - J— [e cos <f> . ds . 

J D + E cos <f> ^ J DJ D 2 J ^ 

Now 

J E cos <f>ds = ^ v cos (f>ds , 



where the integral expresses, for a complete circuit, the circulation of the 
medium in the sense introduced by Lord Kelvin into Hydrodynamics. 
Here a circuit can be completed by any unvaried return path. Now, in 
coplanar Kinematics, the circulation round the contour of any area is 
|2cod(area), where co is the velocity of differential rotation or the vorticity. 
When co is uniform, the time of passage of the ray is, for a ray in the plane 
of motion, 

S T = A (length) - CyL (area). 

Now, when the length is maintained constant, S (area) = 0 for all possible 
variations when the curve is a circular arc. Therefore, as Mr Anderson 
reasons, when the length also is allowed to vary 

S(area) = AS(length), 

where the value of A can be calculated from the circular form. A particular 
circular arc can then he selected which will make St vanish for all small 
variations of its form without restriction to constant length ; and this will 
be the path of an unconstrained ray. 



76 



Proceedings of the Royal Society of Edinburgh. [Sess. 



If an additional uniform velocity is imposed at right angles to this 
coplanar (or rather uniform laminar) motion, the vorticity will remain 
unaltered ; thus, in the expression for St (the ray being now free of 
any restriction to a plane) the area that occurs will be that of the 
projection on the plane of the laminar motion. Now, even in the most 
general coplanar motion, when the vorticity is not uniform, Jo)c£(area) 
will be stationary for small variations which leave the length unvaried, 
only when the curve is a geodesic on the cylinder, perpendicular to 
the laminar motion, on which it lies; for otherwise a displacement of 
the curve, considered as a thread, on the cylinder will make it slack, 
and the cylinder can be expanded to take in more area. This geodesic, 
as it would unroll into a straight line, will have the length of its projection 
on the plane of the laminar motion unvaried while the shape of the cylinder 
thus varies. The shape of the cross-section of the cylinder on which the 
ray lies will therefore be such that for given length of its arc Jwd( area) 
is stationary. In particular, if co is uniform, it will be an arc of a circle.* 
This brings us to Mr Anderson’s result, in a somewhat extended form. 

If a uniform material medium is in motion through the aether with 
vorticity co restricted to be constant in magnitude and direction, all rays 
of light travel in it along helices traced on cylinders of constant radius 

C fl 

2co ju 2 —l 
vorticity. 

* The same argument establishes that a flexible conductor carrying an electric current 
in a uniform magnetic field will when free assume the form of a circular helix ; ef. Proc. 
Lond. Math. Soc., vol. xvi., 1884, p. 169. 



cos'll, having their axes in the direction of the constant 



(Issued separately March 20, 1914.) 



1913-14.] 



Principia Atmospherica. 



77 



IX.— Principia Atmospherica: a Study of the Circulation of the 
Atmosphere. An Address delivered at the request of the Council 
before the Royal Society of Edinburgh, on 1st December 1913. By 
W. N. Shaw, LL.D., Sc.D. , F.R.S., Director of the Meteorological 
Office, Reader in Meteorology in the University of London. 

(Read December 1, 1913. MS. received December 12, 1913.) 

Introduction. 

Every science has two aspects or two stages in its development. In the 
first, the inductive stage, observations are made and compiled, and axioms or 
laws are laid down. In the second or deductive stage the laws are applied 
by syllogistic reasoning, mathematical or otherwise, to elicit conclusions 
which either disclose new facts or show the inevitable connection between 
facts already known, and, in either case, complete the claim of the study to 
the rank of a science. 

The different sciences vary greatly in the stage of development which 
they present. The science of geometry has almost forgotten the origin of 
its own laws and axioms, and occupies itself with the most complicated 
deductive propositions, the forms of which are used to guide the deductions 
of other sciences. Biology is still in the inductive stage: no one ventures 
yet to predict in what form the horse will be found a million or even a 
thousand years hence. 

These different aspects of science appeal with different force to different 
types of human mind. Observers are comparatively rare ; true inducers, 
those who have the patience and the insight to arrange the facts and 
formulate the underlying laws, are extremely rare; deducers, those who 
draw conclusions, not always mathematical or strictly logical, make up the 
balance of the human race. 

Many years ago, in 1862, Dr Alexander Buchan, in a contribution to this 
Society which was subsequently elaborated in a volume of the results of 
the Challenger Expedition, laid the foundations of our inductive know- 
ledge of the atmospheric circulation by a series of maps of the distribution 
of pressure over the surface of the globe. With great pleasure I take the 
opportunity afforded to me by your invitation to address you on recent 
developments of the science of meteorology, particularly in the investigation 
of the upper air, to put before you a representation of the knowledge of 



78 



Proceedings of the Koyal Society of Edinburgh. [Sess. 

the atmospheric circulation as it presents itself to my mind, arranged in the 
normal scientific form, with axioms which represent inductive laws, with 
postulates or lemmas which represent groups of observed facts, and with 
propositions leading to conclusions which are susceptible of verification. 

Synopsis. 

Section I. — Axioms or Laws of Atmospheric Motion. 

1. The Law of the Relation of Motion to Pressure. 

In the upper layers of the atmosphere, the steady horizontal motion of the air at any 
level is along the horizontal section of the isobaric surfaces at that level, and the velocity is 
inversely proportional to the separation of the isobaric lines in the level of the section. 

2. The Law of the Computation of Pressure and of the Application of the Gaseous Laws. 

The pressure at any point in the atmosphere and at any instant is the weight of the 
column of air which stands upon one unit of horizontal area containing the point. The 
numerical values of pressure, temperature, and density at any point of the atmosphere are 
therefore related by the usual formulae for the gaseous laws. 

3. The Law of Convection. 

Convection in the atmosphere is the descent of colder air in contiguity with air relatively 
warmer. 

4. The Law of the Limit of Convection. 

Convection in the atmosphere is limited to that portion of it, called the troposphere, in 
which there exists a sensible fall of temperature with height. The upper layer of the 
atmosphere, in which there is no sensible fall of temperature with height and therefore no 
convection, is called the stratosphere. 

5. The Law of Saturation. 

The amount of water vapour contained in a given volume of air cannot exceed a certain 
limit, which depends upon the temperature and upon nothing else. 



Section II. — Lemmas or Postulates. 

Lemma 1. — In the stratosphere, from 11 kilometres upwards it is colder in the high 
pressure than in the low pressure at the same level; and in the troposphere, from 
9 kilometres downwards to 1 kilometre, it is warmer in the high pressure than in the low 
pressure at the same level. [W. H. Dines, M.O., 2106.] 

Lemma 2. — The average horizontal circulation in the Northern hemisphere in January 
between 4 kilometres and 8 kilometres consists of a figure-of-eight orbit from west to east 
along isobars round the pole, with lobes over the continents and bights over the oceans. 

The average circulation at the surface is the resultant of the circulation at 4 kilometres 
combined with a circulation in the opposite direction of similar shape due to the distribution 
of temperature near the surface. [L. Teisserenc de Bort, Ann. du Bureau Central Mete'oro- 
logique , 1887 ; and W. N. Shaw, Proc. Roy. Soc ., vol. lxxiv. p. 20, 1904.] 



1913-14.] Principia Atmospherica. 79 

Section III. — Propositions. 

Proposition 1 . — To define the conditions for the persistence of the existing motion of the 
atmosphere. 

Proposition 2. — To show that the rate of increase of pressure-difference per kilometre 

of height is 34 - 2 L ( ^ ^ ) ; and hence that the distribution of pressure in the strato- 

& 6 \ d p) * 

sphere is the dominant factor in the circulation of the air at the surface ; that the inter- 
mediate layers between 4 kilometres and 8 kilometres exert little influence upon the 
distribution of pressure. 

Proposition 3.- — To show that the wind velocity across the slope of pressure at any level 
is proportional to 0 ; and thence to show how to utilise observations of the pressure 

and temperature to calculate the wind velocity at any level. 

Proposition 4. — To show that the wind velocity generally increases with height until the 
substratosphere is reached, and falls off with increase in height in the stratosphere. 

Proposition 5. — To show how the distribution of pressure and temperature in the 
upper air can be calculated from the observations of structure represented by a sounding 
with a pilot balloon, and thence to account for the local distribution of rainfall when an 
upper current from the north-west crosses a lower current from the south-west. 

Proposition 6. — To account for the average general circulation over the Northern 
hemisphere in the four-kilometre level as set out in Lemma 2. 



Section I. — Axioms or Laws of Atmospheric Motion. 

The time has arrived when it seems possible and desirable to formu- 
late the laws and principles which can be effectively employed at the 
present day in the explanation of many of the recognised phenomena of 
the structure and circulation of the atmosphere, and to illustrate their 
application. These laws and principles are the result of observations some- 
times suggested or controlled by theory. They are of the nature of 
axioms or inductions, about the validity of which a good deal of discussion 
is possible. Into that discussion I do not now propose to enter. The 
axioms really depend for their justification upon their effectiveness in 
explaining observed facts. They are set out as follows : — 

1. The Law of the Relation of Motion to Pressure. 

In the upper layers of the atmosphere, the steady horizontal motion 
of the air at any level is along the horizontal section of the isobaric 
surfaces at that level, and the velocity is inversely proportional to the 
separation of the isobaric lines in the level of the section. 

The line of argument in favour of this law, which cannot strictly speak- 
ing be either verified or contradicted by any available process of observa- 
tion, is as follows : The condition specified in the law is the condition of 



80 



Proceedings of the Royal Society of Edinburgh. [Sess. 

kinematic equilibrium towards which all atmospheric motions tend, and 
have tended either since the earth began to rotate as it does now, or the 
atmosphere was first formed, whichever of those events is the later in time. 
Any deviation from the equilibrium state is by infinitesimal steps during 
which readjustment to the equilibrium condition has been taking place 
automatically. Hence any finite difference from the equilibrium state can 
only occur in quite exceptional conditions. Consequently if there is an 
ascertained difference from the equilibrium condition it requires explanation 
just as the divergences from the uniformity contemplated by the First Law 
of Motion require explanation. 

An allowance for “ curvature of path ” is one of the differences of which 
account may have to be taken. Its importance depends upon the latitude. 
For* the half of the globe north of 30° N. and south of 30° S. it is generally 
negligible, but near the equator it becomes the paramount consideration in 
the question of the persistence of distribution. Thus rotary systems, small 
or large, are the only possible isobars for a synchronous chart of an 
equatorial region, if one were drawn. The long sweeps of “ parallel isobars ” 
with which we are concerned in this paper would be inadmissible there. 

Near the surface there is always a component of motion along the 
gradient from high pressure to low pressure. In this region the friction 
due to obstacles and to the viscosity of the air prevents the steady state 
being reached, and in consequence the centrifugal force due to the 
velocity of motion is not adequate to balance the pressure. 

This modification of the general principle in the case of surface air may 
be inferred from the fact that in all maps of the distribution of pressure 
and wind at the surface there is evidence of a flow across the isobars. 
The maps are not always conclusive, as they are for sea level and not 
station level ; but no person of experience will doubt the general truth of 
the statement, which in books often takes the form of postulating con- 
vergence towards centres of low pressure and divergence from centres of 
high pressure. 

2. The Law of the Computation of Pressure and of the Application of 

the Gaseous Laws. 

The pressure at any point in the atmosphere and at any instant is 
the weight of the column of air which stands upon one unit of horizontal 
area containing the point. 

This principle assumes that the motion of the air is so slow that the 
hydrostatical forces are not interfered with. Explosion or elastic wave- 
motion would invalidate the law. It therefore assumes that the 



81 



191 3-14. J Principia Atmospherica. 

atmosphere is free from explosions and elastic wave-motions, or that their 
effect is so small that it does not enter into meteorological calculation. 

It follows that the numerical values of pressure, temperature, and 
density at any point of the atmosphere are related by the usual formulae 
for the gaseous laws. In other words, when due allowance is made for 
the difference of composition in consequence of the variation in the amount 
of water vapour or other possible causes, the relation p = ROp holds, where 
p, 0 , p are the pressure, temperature (on the absolute scale), and density of 
the air, and R is a “constant” which is altered by an alteration in the 
composition of the air, but not by other causes. 

3. The Law of Convection. 

Convection in the atmosphere is the descent of colder air in con- 
tiguity with air relatively warmer. 

The law is advisedly stated in this form (although objections may be 
taken to it for want of strictness) because the driving power of the 
convective circulation comes from the excess of density of the descending 
portion, and the excess of density in atmospheric air is due in nearly all cases 
to low temperature. Differences of density might be caused by differences 
of pressure or by differences in the amount of moisture contained in equal 
volumes. But finite differences of pressure cannot persist in contiguous 
masses of air ; the amount of water vapour in air at the ordinary tempera- 
tures with which a meteorologist has to deal is only a small fraction of the 
whole mass, and the colder the air is, the less water vapour is required to 
saturate it. Consequently, although it would be possible in a physical 
laboratory to display a sample of air which, though warmer, is yet denser 
than another cooler sample on account of the humidity of the latter, the 
conditions would not easily occur in nature, and the motive power for 
convection would be exceedingly small. Such cases may therefore be left 
out of account, and we may consider that, of two contiguous masses of air, 
the colder is the denser. 

The law of convection is usually stated with regard to the warmer 
part of the convective circulation, and takes the briefer form that warm 
air rises. The general adoption of this briefer form is due to the fact that 
the warming of air at the surface is a matter of common knowledge, and it 
occurs in the daytime, when its effects in producing a local convective 
circulation are often quite distinctly visible. The form which is adopted 
here, however, is preferable, because in any case it is the cooler and heavier 
air in the neighbourhood which must be looked for if the true cause of 

the circulation is to be found ; and, although on the smaller scale the 

VOL. xxxiv. 6 



82 



Proceedings of the Royal Society of Edinburgh. [Sess. 

heavier air is not far to seek, it is not so easily identified on the scale of a 
meteorological chart. 

Convection in the atmosphere may also be due to the variation in 
the gravitational acceleration due to the motion of the air with reference 
to the earth. 

The gravitational acceleration depends partly on the statical attraction 
of the earth’s mass and partly on the centrifugal action due to rotation. 
The ordinary values of the constant of gravitation assume the rotation to 
be that of the solid earth, and the acceleration of gravity upon air moving 
over the earth’s surface is consequently different from that for calm air. 
Hence the air which forms part of a westerly wind is specifically lighter 
than air at the same temperature and pressure which is calm ; and, on the 
other h^tnd, air which forms part of an easterly wind is specifically heavier. 
These variations in what, contrary to the usual convention, may rightly be 
called the “ specific gravity of the air ” have not yet been generally taken 
into account in meteorological practice, but they are of real significance, 
and are the subject of certain classical papers by von Helmholtz and 
Brouillin on the circulation of the atmosphere. 

4. The Law of the Limit of Convection. 

Convection in the atmosphere is limited to that portion of it in which 
there exists a sensible fall of temperature with height. 

This portion, which comprises about three-fourths of the atmosphere, is 
called the troposphere , and is a layer of air about 10 kilometres thick 
surrounding the whole earth. It is surrounded by an outer spheroid of 
air comprising the remaining fourth part of the atmosphere, which is 
called the stratosphere , in which there is no sensible fall of temperature 
with height. The boundary between these two layers is not at a fixed 
height ; it is apparently a flexible, and therefore deformable, surface, but it 
is not penetrable by air. 

The height of the boundary differs in different latitudes, being highest 
over the equator and getting gradually lower towards the poles ; it differs 
also in different localities, being higher over an area of high pressure than 
over one of low pressure. The local differences are due to deformations of 
the boundary by the accumulation or withdrawal of air from underneath. 
At any place the boundary oscillates about a mean position which should 
be regarded as the height of the boundary of the stratosphere for the 
place. There is no physical reason why the boundary of the stratosphere 
should not be penetrated. All that is required to produce that effect is an 
accumulation of air warm enough to cause upward convection. All that 



1913-14.] Principia Atmospherica. 83 

can be said is that there is no example of the approach to such an ac- 
cumulation. There are a sufficient number of examples in which there is 
a reversal of fall of temperature just below the stratosphere, and these 
show that the stratosphere has, if anything, a little to spare in the way of 
resistance against penetration. Hence, from the point of view of meteoro- 
logical theory we regard the stratosphere as impenetrable. 

5. The Law of Saturation. 

The amount of water vapour contained in a given volume of air 
cannot exceed a certain limit which depends upon the temperature and 
upon nothing else. 

This is really simply a statement of Dalton’s law of the saturation of a 
gas with the vapour of a liquid, but it is quoted here partly because it 
refers to the only form of variation in chemical composition to which the 
meteorological atmosphere is subject, and also partly in order to avoid a 
misapprehension that is very widespread. It is a well-known physical 
principle that when a vapour is condensed the “ latent heat of vaporisation,” 
which, in the case of water vapour, is very large, is liberated. The state- 
ment of the principle is not complete ; it should go on to say that the 
condensation cannot take place unless provision has been made for dispos- 
ing of the heat which will be liberated. In the case of the atmosphere it 
is often assumed that no provision of the kind is required, and that the air 
will, in consequence, be warmed by the heat set free. Herein lies the mis- 
apprehension. Vapour of water in air will not condense unless the air is 
cooled, and the amount of condensation will be limited by the amount of 
the cooling. 

It should, however, be noted that the wording of the law as here given, 
namely, that the limiting amount of water vapour depends upon the 
temperature and upon nothing else, implies a statement about the atmo- 
sphere about which it is necessary to be explicit. Since Dalton’s law was 
enunciated, the researches of Aitken and others have shown that the cooling 
of a mass of air below the “ saturation point ” causes condensation only if 
there are nuclei upon which drops of water can form. In the absence of 
such nuclei, laboratory experiments have shown that condensation does not 
take place until the limits of saturation have been largely exceeded ; “ four- 
fold saturation ” is necessary in such a case. Air without nuclei cooled 
below its “ saturation point ” is said to be supersaturated, and the statement 
of the law of saturation as set out implies that supersaturation does not 
exist in the free air. This is another case in which there is no physical 
reason to prevent anyone imagining circumstances in which supersaturation 



84 



Proceedings of the Royal Society of Edinburgh. [Sess. 

might exist ; all that can he said is that no such circumstances have been 
demonstrated, and the ready formation of clouds at all heights seems to 
indicate that such circumstances are quite unlikely. Hence the meteoro- 
logist is entitled to infer, as the result of a meteorological though not of a 
physical law, that condensation in the form of cloud, or if necessary of 
rain, will always accompany the reduction of temperature of the air below 
the point of saturation, and the amount of condensation will depend upon 
the reduction of temperature and upon nothing else.* 

These five laws express the special principles with which the meteoro- 
logist must approach the consideration of the circulation of the atmosphere, 
with all its complexities and its perplexities. The rest must depend upon 
the application of the ordinary principles of dynamics and physics to the 
results of observations which indicate the pressure, temperature, and density 
of the air in its actual condition when under consideration. It is my object 
in this paper not to discuss or to justify these principles, but to show how 
far they lead us in the explanation of some of the more general phenomena 
of the atmospheric circulation. 

The form which has been adopted for this communication has been 
chosen for the purpose of drawing a distinction between the inductive, the 
observational, and the deductive aspects of the questions which are treated. 
Just as, in the cases of motion treated in text-books of dynamics, there is 
ample opportunity for discussion as to the form of words which shall be 
used for the laws of motion and the grounds for their acceptance or re- 
jection, starting from the consideration that there never has been an actua] 
example of a body free from the action of force, so, in the case of atmo- 
spheric motion, there is no lack of opportunity for the discussion of the laws 
as here set out, starting from the consideration that no actual case can be 
quoted in which we are certain that the laws are strictly obeyed. And 
further, just as in the case of the dynamics of the heavenly bodies the 
whole subject is reduced to a manageable form by setting out to explain 
the changes of motion and their causes instead of pondering over the 
ultimate origin and cause of the state of motion which exists at any 
particular epoch, so in the study of the circulation of the atmosphere we 
may profitably turn our attention to the changes in the motion related to 
the varying distributions of pressure, and leave for the time being the 
endeavour to give a short answer to the question, “ What is the ultimate 

* The supersaturation of atmospheric air is discussed in Dr Alfred Wegener’s Thermo- 
dynamik der Atmosphare, Leipzig, J. A. Barth, 1911. Humidities, by the hair hygrometer, 
up to 107 per cent, are cited on p. 254 of that work. 



85 



1913-14.] Principia Atmospherica. 

cause of any given distribution of pressure, with its attendant atmospheric 
motion ? ” 

We proceed, therefore, first to define in two lemmas the average con- 
dition of the atmosphere which we wish the reader to keep in mind, and 
secondly to apply the laws which have been already enunciated to make 
certain deductions or establish certain propositions with regard to the 
circulation of the atmosphere, which are set out in the synopsis. 



Section II. — Lemmas or Postulates. 

Lemma 1. 

In the stratosphere from 11 kilometres upwards it is colder in the 
high pressure than in the low pressure at the same level ; and in the 
troposphere, from 9 kilometres downwards to 1 kilometre, it is warmer 
in the high pressure than in the low pressure at the same level. 

Proof . — Table of average values of pressure and temperature at different levels over high 
pressure (1031 mb.) and low pressure (984 mb.) at the surface ; with pressure differences 
and temperature differences at each level. Compiled from the diagram and tables of 
W. H. Dines, F.R.S., in Geophysical Memoirs , No. 2, M.O. Publication, 2106. 



Table I. 



Pressure. 


Diff. 


Diff. 


Temperature. 




Low 


High 


A p 


A0 


Low 984 mb. High 1031 mb. 


K. 


mb. 


mb. 


mb. 


°A. 


°A. 


°A. 


15 


116 


123 


7 










14 


135 


146 


11 


- 


9 


224 


215 


13 


157 


171 


14 


- 


11 


226 


215 


12 


183 


201 


18 


- 


8 


225 


217 


11 


212 


235 


23 


- 


4 


225 


221 


10 


247 


273 


26 


+ 


1 


225 


226 


9 


288 


317 


29 


+ 


7 


226 


233 


8 


335 


366 


31 


+ 


13 


227 


240 


7 


388 


422 


34 


+ 


15 


232 


247 


6 


449 


483 


34 


+ 


14 


240 


254 


5 


516 


552 


36 


+ 


13 


248 


261 


4 


591 


628 


37 


+ 


12 


255 


267 


3 


675 


713 


38 


+ 


9 


263 


272 


2 


767 


807 


40 


+ 


8 


269 


277 


1 


870 


913 


43 


+ 


4 


275 


279 


0 


984 


1031 


47 


+ 


3 


279 


282 



Standard deviation of P 9 13 -8 mb. 

Standard deviation of P s 14T. 

Correlation coefficient between the variations of P 9 and P s from the means for the 
month (English ascents) ‘80. 

The table which is here given summarises the results of an important 
investigation by Mr Dines into the relation between the changes of pressure 



86 



Proceedings of the Royal Society of Edinburgh. [Sess. 

at the 9-k. level and the corresponding changes at the surface. The 
changes which he dealt with were chronological, and I have extended the 
conclusion in applying it to topographical differences. This extension is 
justified if the places between which the differences are to be taken are 
sufficiently close together to be influenced by the same barometric system, 
and if the chronological sequence is followed in individual cases. That the 
latter condition is generally satisfied is shown by the high correlation 
coefficient between the variations at 9 k. and at the surface. 

The conclusion as to the relation between temperature and pressure in 
the upper air which is drawn from this table is supported by the gradual 
evolution of meteorological ideas on the subject. Originally it was assumed 
that high pressure meant relatively dense air and low pressure relatively 
light air from the surface upwards. Sometimes temperature and sometimes 
moisture was held accountable for the levity; but the view first put 
forward by von Hann that, in ordinary circumstances, the air over high 
pressure is warmer than that over low pressure has gradually developed 
until it may now be regarded as an accepted principle in meteorology. It 
is borne out by the simultaneous soundings which have occasionally been 
obtained from places within the same barometric system ; and apparently 
the disturbances in the specified order are mostly confined to the lowest 
reaches of the atmosphere. This last point also is well illustrated by the 
figures of the table, which show a gradual falling off, on the average, of the 
temperature differences in the lowest three kilometres. 

Lemma 2. 

The average horizontal circulation in the Northern hemisphere in 
January between 4 kilometres and 8 kilometres consists of a figure-of- 
eight orbit from west to east along isobars round the pole, with lobes 
over the continents and bights over the oceans. 

The average circulation at the surface is the resultant of the circula- 
tion at 4 kilometres combined with a circulation in the opposite direction 
of similar shape due to the distribution of temperature near the surface. 

[L. Teisserenc de Bort, Ann. du Bureau Central Meteorologique, 1887 ; 
and W. N. Shaw, Proc. Boy. Soc., vol. lxxiv. p. 20, 1904.] 

This lemma is introduced in order to supply the reader with a suitable 
general picture of the atmospheric circulation in the upper air, and the 
modification which it must undergo in the lowest layers in consequence of 
the distribution of temperature near the surface. As will be seen from 
Proposition 2, which follows, the similarity of pressure-distribution at all 
heights depends upon the equality of A 6/0 and Ap/p. Consequently, a 



1913-14.] Principia Atmospherica. 87 

circulation along parallels of latitude from west to east in which the air 
nearer the poles is the colder is a circulation which may remain practically 
identical at all heights, and is suggestive of durability and persistence. 

The distribution of pressure at the 4-k. level given by M. Teisserenc de 
Bort suggests that the actual circulation in the upper air is not a circu- 
lation along parallels of latitude, but yet is an approximation thereto, being 
something intermediate between a circle and a figure-of-eight. 

That the circulation at the 4-k. level remains of the same general character 
up to the 8-k. level is suggested by the fact that in those regions distribution 
of temperature is such as to cause very little change in pressure-differences, 
in accordance with the formula of Proposition 2. 

It may be remarked that the distribution was calculated by M. L. 
Teisserenc de Bort from the distribution of pressure and temperature at 
the surface, and is subject to two uncertainties : first, the reduction of the 
original pressure readings to sea-level ; and secondly, their further reduc- 
tion to the 4-k. level. The uncertainties arise from the uncertainty in the 
values of the temperature of the air “ below the ground ” in the reduction 
to sea-level, and above the ground in the reduction to the 4-k. level. To a 
certain extent these two uncertainties compensate each other in the 
important features of the result, and the conclusion as to the circulation 
at which M. Teisserenc de Bort had arrived, is supported by the results of 
Hildebrandsson’s discussion of the international cloud observations (see 
Hildebrandsson and Teisserenc de Bort, Les Bases de la Meteorologie dyna- 
mique, vol. ii., Gauthier- Villars, Paris), and by other considerations of a 
more general character. 

The statements of these two lemmas are based upon observation and 
are, therefore, liable to modification or correction in detail as the results of 
observation become more conclusive. They are, however, sufficiently well 
established to justify their use in the further consideration of meteoro- 
logical problems. 

Section III. — Propositions. 

We now proceed to the consideration of the propositions which are set 
out in the Synopsis. I shall deal in detail with only three of the pro- 
positions, numbered 1, 5, and 6 respectively, because the remaining three, 
numbered 2, 3, and 4, have already been dealt with in a paper communicated 
to the Scottish Meteorological Society, with the title of “ The Calculus of 
the Upper Air, and the Results of the British Soundings in the International 
Week of May 5-11, 1913.” The paper is published in the Journal of the 
Society for 1913. 



88 



Proceedings of the Royal Society of Edinburgh. [Sess. 



Proposition 1 . — The Conditions necessary to maintain a Steady 
Atmospheric Current. 

The conditions which must be complied with if a steady current is to 
be persistently maintained must satisfy the first law, the law of relation of 
motion to pressure. 

The law prescribes that the velocity V is related to the pressure 
gradient y, density p, latitude X, and the angular velocity of the earth’s 
rotation w, by the equation 

F=y/(2a>p sin X). 

Provided that the latitude X remains constant during the persistence of the 
current, this condition presents no difficulty ; the flow will always be de- 
termined by the distance apart of the isobars, but the auxiliary condition 
that the current shall not change its latitude implies that the isobars are 
parallel to the circles of latitude. Hence we may infer that, neglecting a 
very small correction for curvature, a circulation round the pole along 
isobars parallel to the circles of latitude is a “ steady ” circulation which 
will be persistently maintained. The only forces which will interfere with 
it are frictional forces due to the relative motion of adjacent layers of air, 
and, except in the immediate neighbourhood of the ground where friction 
is aided by turbulent motion, these are extremely small. Hence a west-to- 
east circulation or an east-to-west circulation in the upper air, once steady 
will remain so, unless it is disturbed by changes of pressure- distribution. 

But, on the contrary, when the air movement is from south to north 
or from north to south, or has any component which gives a motion across 
the circles of latitude, a change in sin X has to be dealt with. 

Motion from South to North. 

We propose to deal first with a current moving from south to north. 
We shall suppose the current to be uniform over the section from the one- 
kilometre level upivards. We leave out the lowest kilometre because we 
know that it is disturbed by quasi-frictional forces at the surface. 

In this case the value of sin X is increasing, and therefore greater pressure- 
difference is required to get the same quantity of air through the same 
section. But the pressure-difference is limited by the isobars, which are by 
hypothesis supposed steady. Any convergence of the isobars themselves 
provides its own remedy, because the gradient velocity is inversely pro- 
portional to the distance. We have, therefore, only to deal with the 
change in sin X in the formula 

F=y/(2 mp sin X). 



1913-14.] 



Principia Atmospherica. 



89 



Let L be the width of the current, and H its depth ; then the flow over the 
whole section Lx H is LHV ; and by the equation of continuity this must 
be constant as the stream flows northward. 

Now 

LHV= n HLy , 

2(0/0 sin A. 

and Ly is the pressure-difference, A p, between the two sides of the current. 
LHV is constant ; hence, differentiating, we get 

q _ dH dp d sin A 
~H~J 
or 



sin A 



d JLJ± + C otX0X. 

H p 

Now p can only alter by variation of pressure, temperature, or composition ; 
change of pressure is ruled out because the motion is along isobars ; change 
of temperature will be very slight because there is no change of pressure, 
and there are no other causes of any appreciable change of temperature ; 
and change of composition can only occur in consequence of condensation. 
By Law 5, in the absence of change of temperature no change of composi- 
tion will occur. Hence 

dp/p = 0, 

and 

— cot ASA. 

H 

Ln other words, the thickness of the moving layer must increase fractionally 
by the amount cotXSX for the change of latitude <5A. If latitude is ex- 
pressed in degrees and not in circular measure as differentiation supposes, we 

must introduce the factor and thus the formula becomes 

180 

4 ^=-0175 cot A. 

H aX 

Hence, in order that a current may persist over any stretch from south to 
north, it is necessary that the thickness of the moving layer should increase 
fractionally to the extent of '0175 cot \ for every degree of latitude which 
it crosses. 

We have assumed the layer to be unlimited above, and limited below by 
the one-kilometre level. To provide for the additional air by increasing 
the height above the selected base-level would result in altering the 
pressure : that mode of operation is therefore excluded by the condition of 
maintenance of the current as steady. Consequently we must suppose the 
additional thickness to be provided by encroachment upon the lowest 



90 



Proceedings of the Royal Society of Edinburgh. [Sess. 



kilometre : that region is already supposed to be occupied by an extension 
of the current which is disturbed by surface friction ; hence, unless there is 
a continual flow-off of air from below the one-kilometre level, the steady 
state cannot be maintained. 

The south-to-north current implies a high pressure on the eastern side 
and a low pressure on the western side, and near the surface there is a 
component of flow from high to low across the isobars. Hence we may 
suppose a case in which the northward-flowing current is maintained steady 
by the flow-off from east to west in the surface layer. We proceed to 
calculate the amount of this east-to-west current which will suffice to draw 
off the increase of the current above 1 kilometre. 

We suppose, for the purpose of calculation, that the east-to-west com- 
ponent is uniform over the lowest half kilometre of the western section. 
The fractional increase of thickness in the upper layer has been shown to 
be ’0175 cot X for each degree of advance northward. The increase of the 
thickness is the same over each elementary layer of height into which the 
whole thickness can be divided ; consequently the air to be removed is the 
fraction -0175 cot X of the transverse vertical section at every level. If 
the removal is confined to the lowest half kilometre, which contains a 
fraction of the atmosphere approximately one-twentieth of the whole, it 
follows that a fraction 20 x ‘0175 cot X of the lowest half -kilometre layer 
has to be removed for each degree of advance northward. 

For each metre of advance northward, therefore, a fraction ^ X 0175 cot X 

llTlxlO 3 

of the lowest half-kilometre layer has to be removed ; and, similarly, for 

each metre per second of the wind velocity from south to north a fraction 

20 x -0175 cot X i t i 7 

— — — — — must be removed every second. 

-L JL _L I X JL v/ 



Suppose that the breadth of the advancing current which is supposed 
to be maintained steady is L kilometres, the westerly flow at the western 
end of the lowest half kilometre must carry away air at the rate of 

20 x 0175 cot X x l kilometres per second, or there must be a cross com- 
UlTxlO 3 



ponent of wind there amounting to 



20 x *0175 cot X 
HIT 



xL metres per second. 



If the cross wind be referred to the width of a current expressed in 
degrees of longitude at the latitude X, and if l be the width of the current 
in degrees, we get 

L = 111T cos XL 



Whence it follows that in order to maintain a south-to-north current of V 



91 



1913-14.] 



Principia Atmospherica. 



metres per second there must be a cross wind leaving the lowest half 
cos 2 A 

kilometre of "35 — IV metres per second. 

sin A 

We have supposed the drainage to take place entirely in the lowest 
half kilometre, which represents one-twentieth of the atmosphere. The 
same result might be produced by a distributed cross-flow throughout the 

western vertical section of the moving air of *0175 C - ? S ^ P metres per second. 

We may therefore sum up the conclusion as follows: — 

In order that a current across circles of latitude from south to north 
with a breadth of l degrees of longitude may 'persist unaltered at any level, 
it is necessary that air should be drawn away from the moving air at that 

level to the extent of *0175 CQS ^ IV metres ver second. 

sin A 

The use of the surface layer, to draw off the excess of air which would 
otherwise prevent the persistence of a current across circles of latitude, is 
quite appropriate in the case of currents with a south-to-north component. 
According to the rider to Law 1, such a current certainly exists, and it only 
requires its magnitude to be adjusted in order that persistence may be secured. 
Fora current extending over 10° of longitude in lat. 45° the cross component 



CROSS SECTION OF 9 Kl LO MET RES &K.TO 10K] OF 
A S. TO N.CURRE NX 5'WIDE'MAINTAINECT IN LATHS' 



w 



DOWNWARD FLOW. OF 0175 
*TMOSP"£f?r FOR each Decker 
OF L AT n UOC CR OSS CO 






K 5* LO/VG: il 

Fig. 1. 



at the extreme west of the lowest half kilometre would have to be two 
and a half times the steady south wind above, and that hardly occurs in 
practice ; but there are a variety of ways of accounting for any discrepancy 
between the calculated and observed cross-wind in case the south-to-north 
current is actually maintained. Hence the diagram, fig. 1, representing 
the conditions for maintenance of a south wind across a section of 5° of 
longitude is not unreasonable. 



92 



Proceedings of the Royal Society of Edinburgh. [Sess. 



The representation is, moreover, borne out by the facts which are known 
as to the distribution of temperature in the atmosphere. For the seven 
kilometres between the 1-k. level and the 8-k. level the temperature on the 
“ high ” side is “ too warm,” and therefore represents the effect of a down- 
ward flow while the pressure is maintained.* Hence it seems possible for 
the conditions for the maintenance of a south-to-north current to be realised 
in practice, though the adjustment would be delicate and might certainly be 
transient. 



Motion from North to South. 



Persistence in the reverse of the case just described, that is to say, in 
the case of a current flowing from north to south, is in one respect more 
difficult and in another more easy. 

What we have v to provide for here is not the thickening but the 
shrinkage of the current in consequence of the decrease of sin X as successive 
circles are crossed. The numerical result applies equally, but in the opposite 
sense. Thus a current of velocity V flowing from north to south requires 
that air should be fed w T ith an inflow which, if distributed over the whole 



side, would be *0175 



cos 2 X 
sin X 



IV at any level at which the wind velocity is 



V t in order to avoid fractional shrinkage of *0175 cot X per degree of 
advance. It is more difficult to see how the air could be supplied ; but the 
shrinkage of the current while the distribution of pressure which controls 
it is maintained presents little difficulty if the current in question may be 
supposed to remain an upper air-current and therefore subject only to the 
pressure-distribution appropriate to the current. To explain the persist- 
ence of a current in the lower layers would make greater demands upon 
one’s ingenuity, because the introduction of the necessary air would, as a 
rule, alter the distribution of pressure below, and limitations to prevent 
that alteration would have to be invented. Hence the maintenance of a 
current from north to south at all levels requires some artifice for the 
continuous production of the necessary pressure-distribution. The difficulty 
is further aggravated by the fact that, just as in the case of the south-to- 
north current, there is a flow-off from “ high ” to “ low ” in the surface 
layers ; but unfortunately it flows away from where it is required to make 
up the loss due to change of latitude, and consequently that loss as well as 
the loss by shrinkage has to be made good if the northerly current is to be 
maintained. 

Putting the two currents side by side as in fig. 2, we see that the supply 
* See the paper in the Journal of the Scottish Meteorological Society already referred to. 



93 



1913-14.] Principia Atmospherica. 

for the north-to-south current may possibly come from the surplus of the 
south-to-north current, but it cannot be along the surface. It must be remem- 
bered that, so far as our information goes, we have no reason from observa- 
tions for supposing that the relation between pressure and temperature in a 
northerly current is different from that in a southerly current, though the 
evidence is not quite conclusive, because the former has been less frequently 
the subject of investigation. The air supply ought, therefore, to be carried out 
in a similar manner in both cases. Persistence in this case, therefore, requires 
the surplus of the adjacent southerly current and the outflow from the 
northerly itself both to be delivered to the northerly current in the upper 
layers in order that the proper temperature distribution may be obtained. 



CROSS SECTION OF 9 Kl LOMETRES&K TO lOK] OF 
TWO CURRENTS S. TO N. AND N. TO S. EACH 
5‘ WIDE MAINTAINED IN LAT4 5.' 




Such a combination of circumstances may fairly be regarded as exceptional, 
and therefore the maintenance of a northerly current must be regarded as 
exceptional. 

Changes from the Steady State. 

To complete the process of maintenance of the steady current from the 
north we should have to imagine the whole of the outflow in fig. 2 towards 
the “low” from both sides conveyed to the upper part of the northerly 
current, and thus transferred from low pressure to high pressure as well as 
from low level to high level. It is possible to make out a process with the 
aid of the law of convection if the two currents are at different tempera- 
tures. In such a case the surfaces of equal pressure may be so sloped as to 
produce an apparent flow across isobars from low to high ; but we have no 
such obvious and automatic explanation to give in the case of the northerly 
current as in the case of the outflow of the southerly current. And, 
indeed, it was not intended to adduce the conditions for persistent main- 
tenance with the object of claiming that they are generally satisfied in 
practice. On the contrary, the adjustment of the outflow in the southerly 



94 



Proceedings of the Royal Society of Edinburgh. [Sess. 

current to the conditions of persistence must be fortuitous and unlikely to 
be maintained for long ; the adjustment of conditions for the maintenance 
of a northerly current is even more fortuitous. The reason for setting out 
the conditions of maintenance is rather to show that natural conditions of 
atmospheric currents are not, as a rule, those of persistence but of change. 
If the conditions of persistence which have been set out are not realised, 
the currents will change, and by Law 1 changes in currents imply changes 
in the distribution of pressure. Consequently, an atmospheric system 
which includes northerly or southerly currents has within itself elements 
and causes of change in the distribution of pressure. It is therefore 
unnecessary to attribute all changes to outside causes. It is preferable to 
consider the causes of the changes which are inherent in cases in which we 
cannot suppose the conditions of maintenance satisfied, and to regard 
external causes of change which are known to exist as supplementary. 

It follows that we have not to regard a quiescent atmosphere all over 
the globe as the starting-point of our explanation of the present condition, 
but we have rather to regard the circumstances of transition from one 
set of conditions to another. 

We may add some notes upon practical cases. 

Persistent Southerly Current. 

The maintenance of a southerly current has been shown to be a question 
of adjustment of velocities, and a southerly current lends itself comparatively 
easily to persistence. Examples of a persistent southerly current across 
the parallels of Northern Europe furnish a well-recognised type of weather 
that seems to resist the incursions of cyclones from the west. A southerly 
current often extends throughout the vertical section of the atmosphere, as 
might be expected from the automatic thickening described above. 

Persistent Northerly Current. 

On the other hand, a northerly current requires constant reinforcement, 
and yet a northerly current, persistent for days over the North-Eastern 
Atlantic, is by no means unknown. It is possible that the necessary air 
in this case may be supplied by the gravitational flow of cold air off 
Greenland or Northern Siberia, which must contribute a large amount of 
air to the surface layers above the North-Eastern Atlantic. 

Replacement of a North-Easterly Current by a South-Westerly Current. 

An example of the disturbance of persistence frequently occurs in the 
case of a north-easterly current with a south-westerly current above it, a 



95 



1913-14.] Principia Atmospherica. 

case which is referred to in Mr Cave’s book on the Structure of the Atmo- 
sphere in Clear Weather as a frequent precursor of weather of the thunder- 
storm type, accompanied by the setting in of the south-westerly wind. 
The distribution of temperature is such as to change the direction of the 
pressure-gradient near the surface. Consequently the outflow from high 
to low goes from under the upper “ low ” to under the upper “ high.” The 
necessity for the thickening of the southerly current is therefore not re- 
lieved by the outflow, but accentuated thereby. At the same time the 
north-easterly current has to get thinner, so it is gradually replaced by the 
south-westerly current settling down to the surface. The appropriate re- 
distribution of pressure at the surface accompanies the redistribution of 
air-currents in the vertical section. 

These examples are adduced because it seems not improbable that they 
give us the opportunity of watching the operation of the causes of change 
which are inherent in any actual state of atmospheric motion. 

Let me summarise the attitude which seems to me to be appropriate 
for the meteorologist to take up in face of the complexities of the atmo- 
spheric circulation, by again referring to the position of the astronomer 
before the final enunciation of the laws of motion. Imagine the perplexity 
of the astronomer who, finding the heavenly bodies moving in all sorts of 
directions with all sorts of velocities, set himself to explain the motion 
which each possessed. To him the laws of motion bring the assurance that 
it is not necessary for him to explain why a body moves ; it is the changes 
of motion which should occupy his attention. So the meteorologist, looking 
at the circulation of the atmosphere in obedience to the distribution of 
pressure, has not to ask himself why the pressure is high here or low 
there, but rather, “ Is the distribution persistent, and if not, are the causes 
of change inherent in the existing circulation sufficient to account for the 
changes ? ” If it be said that, after all, the problem remains the same and 
the point of view is immaterial, it is right to remember that in astronomy 
the change in the point of view has simply reduced chaos to law. 

From what has been already said, it appears that a steady state of 
persistent motion of the earth’s atmosphere is in the highest degree im- 
probable, because it can only occur in a combination of circumstances which 
are independently fortuitous ; but it is desirable to call attention to a possible 
case of motion which is quasi-persistent in consequence of two concurrent 
and persistent infractions of the conditions of steadiness. 

If we suppose the south-to-north and north-to-south currents of fig. 2 
placed back to back so as to form an anticyclonic section instead of the 
cyclonic section represented in fig. 2, we find in juxtaposition a south- 



96 



Proceedings of the Royal Society of Edinburgh. [Sess. 

to-north current which must get rid of air, and a north-to-south current 
which must have air in order to maintain itself, and all that is required in 

order to maintain both currents is a transverse flow of *0175 C ? S ^ L IV at 

sm \ 

any level where the current velocity is V from the south-to-north current 
to the north-to-south current. We cannot accept this transverse motion as 
a part of steady motion, because the motion would not be strictly speaking 
along the isobars as prescribed by Law 1. But if we could persistently 
take the momentum necessary for the perturbation of the steady motion in 
compliance with Law 1 out of the general west-to-east circulation, we 



High 











10 








9 


South- 


> 


North - 


8 


to- 


•0175 


to- 


7 


North 


sm a 


South 


6 


current 


1 


current 


5 

4 


V 


•0175^^zr 

Sill A 




3 


‘ ‘ Too warm ” 


> 


‘ ‘ Too warm ” 


2 


I 




1 


1 






1 









<$- - - 1° long. > long. - -> 



Fig. 3. — South-to-North current V 1 supplying its own bottom outflow 
Uj and maintaining a parallel North-to-South current V 2 and its 
bottom outflow U 2 by transference of air across the ‘ ‘ high ” ridge. 

could have both the southerly and northerly currents maintained. It is 
not unreasonable to suppose that, as a westerly circulation has to be 
diverted northward to produce the northward circulation, the westerly 
momentum at the various levels may produce the effect described. In 
this case we should have the permanence of the anticyclonic distribution 
maintained by the persistent infraction of the law of relation of pressure 
to wind. At the same time a flow-off at the bottom outwards in both 
cases has to be supplied, and in consequence there is a downward flow 
under permanent conditions of pressure over both sides of the ridge of 
“ high ” which would give the necessary warming of the air of a high- 
pressure region. Hence the case represented in fig. 3 seems to furnish a 
possible example of a high-pressure region maintained in a quasi-steady 
condition by a transfer of air across the isobars in consequence of the 



97 



1913-14.] Principia Atmospherica. 

uncompensated momentum ; the flow-off on either side at the bottom from 
“ high ” to “ low ” denoted by U 1 and U 2 being provided by the adjustment 
of the currents V 1 and V 2 . 

Whether or not this be a true explanation, it certainly agrees with 
common experience in regarding a high-pressure area as more easily main- 
tained persistently than a “ low. 1 ’ 

Propositions 2, 3, and 4. 

These propositions, which deal with the application of the formula for 
change of pressure-difference with height (the unit of height being the 
metre), viz. 

to explain the dominance of the stratosphere and the lack of importance of 
the troposphere in the distribution of pressure at the surface, to compute 
the wind- velocity from the pressure-difference at any height and to explain 
the observed falling off of wind-velocity with height in the stratosphere, 
have been dealt with in the paper communicated to the Scottish Meteor- 
ological Society, and the work need not be repeated here, especially as 
Proposition 5 makes use of the same equations. 

Proposition 5 . — The Calculation of the Distribution of Pressure and 

Temperature in the Upper Air from the Observations of Structure 

represented by Soundings with a Pilot Balloon. 

A pilot balloon gives primarily the horizontal direction and velocity of 
the wind at successive heights, so that we may suppose that we have the 
horizontal direction and velocity of the wind at each kilometre as the data 
for the calculation. 

The first step is to resolve the wind-velocity into two components, 
west to east and south to north. 

By the application of Law 1 we can then compute the pressure-difference 
for 100 kilometres in the south-to-north direction and the west-to-east 
direction. 

Thus, if A p is the pressure-difference for a distance L taken along the 
direction of the wind velocity V, if 6, in absolute degrees, and p, in milli- 
bars, are the temperature and pressure, X the latitude, go the angular 
velocity of the earth’s rotation, and R the constant of the characteristic 
equation for air, we have 

y_ R 0 Ap _ g 6 Ap 
2o> sin \ p L p L 

And since both velocity and pressure-difference, or gradient, are vector 

VOL. xxxiv. 7 



98 



Proceedings of the Royal Society of Edinburgh. [Sess. 

quantities, we get for the northward and westward components of the 
pressure-gradient per hundred kilometres 

A N y=l|-(WtoE) 

and 

AwP = l^ T( S to N), 

where (W to E) and (S to N) indicate the components of the wind- velocity 
resolved in those two directions. 

Now from a pilot balloon ascent we cannot get the value of p/0 for the 
special occasion of the ascent, but there is really little variation from time 
to time of this ratio. For the greater part of the troposphere variations of 
pressure and temperature go together, and the whole range of variation 
of 0 for any particular time of year is less than 10 per cent., and the whole 
range of variation of p is of the same order. Consequently a mean value 
of p/0 may be taken as a first approximation for the purposes of the 
calculation. 

The following is a table of average values of p/0 : — 



Table II. — Table for Values of p/e at Different Levels — 
Average of Results in “Geophysical Journal,” 1912. 



Height, 

kilo- 

metres. 


p/e. 


Height, 

kilo- 

metres. 


Pie. 


Height, 

kilo- 

metres. 


p/e. 


Height, 

kilo- 

metres. 


pie. 


20 


•26 


15 


•53 


10 


1*18 


5 


2-11 


19 


•28 


14 


•64 


9 


1-35 


4 


2-35 


18 


•32 


13 


•75 


8 


1-52 


3 


2-61 


17 


•39 


12 


•87 


7 


1-70 


2 


2-91 


16 


•46 


11 


1-02 


6 


1-90 


1 

Gd. 


3*24 

3-55 



Having thus computed the pressure-difference for 100 kilometres, in 
two directions at right angles, for the level of each kilometre, we may next 
obtain by subtraction the change of pressure-difference for each kilometre. 
The use of the mean value for p/0 will not altogether invalidate the process, 
because the variation from kilometre to kilometre depends generally on the 
ordinary diminution of pressure with height rather than on any extra- 
ordinary distribution of temperature. 

Substituting the value of the rate of increase of pressure-difference per 
kilometre of height in the equation 

dA P_oA.oP(M A P 
dh~ “ 6\0 p 



99 



1913-14.] Principia Atmospherica. 

and again assuming a value of 0/p, we can compute Ad provided we have a 
value of 6 which can properly be substituted in the equation. 

Here again we must have recourse to the mean value, as we have no 
observation of actual temperature at the time ; but, again, the error made is 
not fatal to the practical success of the calculation, because 0 comes in as a 
factor which affects the scale of the variation ; it does not affect the sign. 
By taking the mean value for the month instead of the actual value the 
error is probably less than 10 per cent., and the whole error of employing 
mean values for actual values probably amounts to less than 20 per cent. ; 
and in considering the distribution of pressure and temperature in the 
upper air we are not yet in a position to reject observations and informa- 
tion which may be in error by as much as a fifth. 

Consequently we may properly use the calculation here indicated to 
give at least a rough but working idea of the distribution of pressure and 
temperature at successive levels in the atmosphere when we know the 
velocity and direction of the wind there. 

The errors in p/0 and 0 are less important in considering the nature of 
the distribution, because the same values, right or wrong, are used for both 
components at the same level. 

The following table of monthly averages gives values which may be 
used in the absence of any special information for the particular occasion : — 



Table III. — Average Temperature at Different Levels for Months. 

1. For British Isles. Taken from “Geophysical Memoirs,” No. 2 (W. H. Dines). 



Height, 

kilo- 

metres. 


Jan. 


Feb. 


Mar. 


April. 


May. 


June. 


July. 


Aug. 


Sept. 


Oct. 


Nov. 


Dec. 


14 


216° 


217° 


219° 


221° 


222° 


223° 


222° 


221° 


219° 


217° 


216° 


215° 


13 


216 


217 


219 


221 


222 


223 


223 


221 


219 


218 


217 


216 


12 


217 


218 


219 


220 


221 


222 


222 


221 


221 


219 


218 


217 


11 


217 


217 


217 


219 


220 


221 


222 


222 


221 


220 


219 


218 


10 


220 


220 


220 


222 


224 


225 


226 


226 


226 


224 


223 


221 


9 


224 


223 


224 


226 


229 


231 


234 


233 


233 


231 


228 


225 


8 


230 


229 


230 


232 


236 


238 


241 


241 


241 


238 


235 


332 


7 


237 


236 


237 


239 


242 


245 


247 


248 


247 


245 


241 


238 


6 


243 


243 


244 


246 


249 


252 


255 


255 


254 


251 


249 


245 


5 


250 


249 


250 


252 


256 


259 


261 


262 


261 


258 


255 


252 


4 


257 


256 


257 


259 


262 


265 


267 


268 


267 


264 


261 


258 


3 


263 


262 


263 


265 


268 


271 


273 


274 


273 


270 


267 


264 


2 


267 


266 


267 


270 


273 


276 


278 


279 


278. 


275 


272 


269 


1 


271 


271 


273 


276 


279 


282 


283 


283 


281 


279 


275 


272 


Gd. 


276 


276 


277 


282 


285 


288 


289 


289 


286 


283 


280 1 


277 



I give in Table IY. a specimen of the calculation as applied to the 
results of a sounding with a pilot balloon on April 29, 1908. 



Table IV. — Computation of Pressure Distribution and Temperature Distribution from 
Pilot Balloon Ascent of April 29, 1908. 



100 






Proceedings of the Koyal Society of Edinburgh. [Se 



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1913-14.] Principia Atmospherica. 101 

I have used this method for the calculation of the distribution of 
pressure and temperature in the cases represented by photographs of models 
in Mr C. J. P. Cave’s book on the Structure of the Atmosphere in Clear 
Weather * which includes that given in detail on p. 100. Some of the 
results are given below — the problem being understood to be stated thus : 
Given the wind-velocity at any point, to find co-ordinates for drawing the 
isobar for the next higher millibar and the isotherm for the next higher 
degree of temperature. It will be remembered that the isobar over the 
point of observation itself is to be taken parallel to the wind direction in 
accordance with Law 1, and the direction of the isothermal lines will be 
taken parallel to the line joining the computed co-ordinates, so that the 
distribution of pressure and temperature is to be represented each by two 
parallel lines, the co-ordinates giving their direction and their distance apart. 



1. Sounding of May 5, 1909, 6h. 43m. p.m. 

“ Solid Current ” ; Wind approximately uniform in direction and velocity 
from 2 kilometres to 10 kilometres. 

Table V. 



Height. 


Distance of next higher 
isobar in kilometres. 


| 

Distance of next higher 
isotherm in kilometres. 


k. 


k. 


k. 


k. 


k. 


9-10 


143 N 


233 E 


93 N 


93 W 


8-9 


143 N 


181 E 


1000 N 


1250 E 


7-8 


123 N 


291 E 


454 S 


54 E 


6-7 


114 N 


292 E 


137 N 


74 W 


5-6 


99 N 


141 E 


100 S 


139 W 


4-5 


77 N 


110 E 


832 N 


58 E 


3-4 


67 N 


187 E 


303 S 


909 W 


2-3 


. 58 N 


144 E 


769 N 


196 W 


1-2 


54 1ST 


353 E 


270 N 


49 E 


0-1 











In this case it is interesting first to notice the gradual separation of the 
isobars with increasing height and consequently diminishing density. This 
is the ordinary condition for the velocity remaining invariable with height. 

Secondly, it is noteworthy that the separation of the isotherms is 
generally large and also very irregular, showing approximate equality of 
temperature in any layer, but great want of conformity between one 
layer and another. Such variations in the distribution of temperature may 
easily be accounted for by local convection producing changes of tempera- 
ture and possibly clouds, and it leads us to reflect that the convection 
* Cambridge University Press, 1912. 



102 



Proceedings of the Royal Society of Edinburgh. [Sess. 

which produces local clouds will also produce local modifications of 
temperature and consequently local modifications of pressure and wind 
velocity. If we ask whether such local variations of temperature and wind 
are at all probable, we have only to refer to the records of the ascents 
of registering balloons and of anemometers, or of pilot balloon ascents, 
to give an affirmative answer. 

Nothing is more noteworthy than the irregular variations in tempera- 
ture-difference as given by a pair of soundings with registering balloons, 
and the curious local irregularities of wind disclosed by pilot balloon 
ascents. Hitherto it has been customary, on quite general grounds, to 
regard them both as possibly due to the uncertainties of observation. We 
now see that they may equally well be important evidence of complication 
in the structure of the atmosphere. 

Those whose temperament inclines them that way have still the 
possibility of uncertainties in observation to fall back upon ; but the better 
plan would seem to be to arrange for simultaneous ascents of registering 
balloons and pilot balloons, so that the actual and computed distribution 
of temperature may be compared. The interesting feature of the compari- 
son would be that, if the method of computation here indicated (with its 
acknowledged uncertainties in taking mean values for p/6 and 0 instead of 
actual values) should prove serviceable, then one pilot balloon ascent gives for 
practical purposes almost as much information as three registering balloons. 

Apart from the uncertainties which have been mentioned, the con- 
clusions as to the distribution of temperature and pressure are incontrovert- 
ible by those who accept Law 1, and per contra if the conclusions are 
sustained Law 1 receives its most complete vindication. 



2 . Sounding of September 1 , 1907 . 
Westerly Wind rapidly increasing aloft. 
Table VI. 



Height. 


Distance of next higher 
isobar in kilometres. 


Distance of next higher 
isotherm in kilometres. 


k. 


k. 


k. 


k. 


k. 


4 


68 S 


oo E or W 


86 S 


119 E 


3 


77 S 


400 W 


44 S 


555 E 


2 


139 S 


294 W 


119 S 


185 W 


1 


196 S 


526 W 


43 S 


80 E 



The increase in the intensity of the pressure-distribution with height 
is clearly shown, and finds its explanation in a steep temperature gradient 
from south to north. 



1913-14.] 



Principia Atmospherica. 



103 



3. Sounding of November 6 , 1908, 10h. 55m. a.m. 

Reversal of Direction from E.S.E. in the lowest three kilometres 
to W.N.W. in the reach from 4 kilometres to 9 kilometres. 



Table VII. 



Height. 


Distance of next higher 
isobar in kilometres. 


Distance of next higher 
isotherm in kilometres. 


k. 


k. 


k. 


k. 


k. 


8-9 


185 S 


356 W 


96 S 


312 W 


7-8 


204 S 


356 W 


416 S 


770 W 


6-7 


200 S 


416 W 


294 S 


189 W 


5-6 


233 S 


435 W 


139 S 


625 E 


4-5 


344 S 


665 W 


101 S 


109 W 


3-4 


5000 S 


4000 E 


119 S 


270 W 


2-3 


588 N 


416 E 


286 S 


108 W 


1-2 


100 N 


142 E 


24 S 


65 W 


0-1 


77 N 


172 E 


34 N 


40 E 



The gradual diminution of velocity up to 4 kilometres, where the 
isobars become very wide apart, is well marked in the second and third 
columns ; and it is seen that the reversal is to be accounted for by a rapid 
rise of temperature to the south-west in the second and third kilometres, 
with a similar distribution of temperature of less marked character in 
the higher layers. 

It will be noticed that in the second and third kilometres, where the 
reversal is determined, the slope of temperature is opposite to the slope of 
pressure, a condition which we have already noticed as being characteristic 
of large change of pressure-difference with height. In the sixth kilometre 
the next higher isotherm is found a long way off on the east instead of on 
the west, as in the layers above and below. The change is not really very 
. large, as the temperature conditions are nearly uniform in that region as 
regards the west-to-east direction, but it furnishes a reminder of the close 
association which we must expect to find between slight changes in 
temperature distribution and in the direction and force of the wind. 



4. Sounding of April 29, 1908. 

North-Westerly Current in the Upper Layers crossing a Lower 
Current from the South- West. 

This is the example of which the details of the working are shown in 
the table on p. 100, and it is one of great interest, because it is characteristic 



104 Proceedings of the Royal Society of Edinburgh. [Sess. 

of the advance of a well-developed cyclonic depression from the westward. 
It has long been recognised, by seamen and other observers of weather, in 
observations of upper clouds which are seen to be moving from the north- 
west while the surface winds are coming from the south-west. It is one 
of the surest signs of the rainfall which occurs in the front of a cyclonic 
depression. The table already given shows the values of A N p and A w p for 
each kilometre level, and the values of A^d and Awd computed from the 
changes in the pressure-differences for successive kilometre steps. We 
may note here an ambiguity of notation, which we ought to find some 
means to remove, and which ought at least to be made clear. In the table 
A p and A# are used to indicate the slope of pressure and of temperature in 
the two directions N. and W. Thus in the table, when A p or Ad is positive 
for a given direction, it is to be understood that it represents the fall of 
pressure in that direction. But the usual convention of the differential 
calculus is that an increase in the quantity represented is indicated by a 
positive value of the difference. The ambiguity arises from the use of the 
convenient symbol A to denote the difference, while the meteorological 
practice is to think of gradient as represented by downward slope. I have 
not found any convenient new symbol to use instead of A to indicate a 
negative difference, so the ambiguity remains for the present, though I feel 
that an apology is due for it. 

In order to present in a table the corresponding values of A p and Ad 
for the same level, I have taken the means of the two values of A p for the 
top and bottom of the kilometre to which Ad refers. This practice is, 
perhaps, rather doubtful, but except in Table VI. it has been followed in 
the tables already given, so I adhere to it in this one. 

Converting by simple inversion the figures for Ap and Ad per 100 
kilometres into distances along the axis of the intercepts of the next higher 
isobar and isotherm respectively, we obtain the following : — 

Table VIII. 



Height. 


Distance of next higher 
isobar in kilometres. 


Distance of next higher 
isotherm in kilometres. 


k. 


k. 


k. 


k. 


k. 


5-6 


84 S 


143 W 


60 S 


102 W 


4-5 


109 S 


263 W 


64 S 


50 W 


3-4 


141 S 


2000 W 


135 S 


132 W 


2-3 


131 S 


526 E 


244 N 


125 W 


1-2 


141 S 


312 E 


93 S 


909 E 


0-1 


200 S 


232 E 


270 S 


222 W 



1913-14.] 



105 



Principia Atmospherica. 

In this table the gradual conversion of a southerly component into a 
northerly component associated with higher temperature to the westward 
is very noticeable. 

It will be seen that the isobars above 4 kilometres are, roughly speak- 
ing, at right angles to those in the lowest kilometre, which is, of course, in 
accordance with the wind observations ; but that the isotherms, with some 
fluctuations, particularly in the second kilometre, are similarly arranged at 
the top and at the bottom. That is to say, the upper winds are flowing 
from the north-west with the higher temperature on the south-west side, 
while the lower winds are moving transversely from the south-west with a 
distribution of temperature parallel to that of the upper air, but in this case 
the isotherms are across the wind. 

These results are represented in fig. 4, which was originally drawn to 
the same horizontal scale as the larger chart of the Daily Weather Report, 
and it is clear that in the lowest stage the columns of warmer air brought 
in by the south-westerly current are being carried underneath the parallel 
columns of the upper current. Up to 4 k., where the wind has become 
westerly, we have a distribution which produces the same effect. The 
wind is always carrying warmer air under colder air, and as, by Proposi- 
tion 1, a southerly current tends to thicken and a northerly current to give 
way, the pushing under of the warmer air becomes more effective, until 
instability occurs and rainfall sets in. The irregularities which are shown 
in the distribution of temperature are probably due to previous convectioii a 

We have here, therefore, the assurance of rainfall conditions as the 
south-westerly wind pursues its course under the north-westerly in front 
of the approaching depression. The rainy condition of that part of a 
depression is thus directly accounted for. 

The characteristic rainfall of a cyclonic depression is generally associated 
with a general convergence of the surface isobars, but this hypothesis is 
difficult to follow into details, because the convergence is general over the 
area, while the rainfall is local. The analysis of the conditions of the upper 
air here set out shows that there is good reason for rainfall in the upper 
layers, to which the doctrine of general convergence cannot safely be held 
to apply. 

To the examples which are taken from Mr Cave’s work, I may add one 
for October 16, 1913, which was reported to me by Mr J. S. Dines in con- 
nection with his work for the branch Meteorological Office at South 
Farnborough. 

On that day, at Pyrton Hill, where the sounding was made, there was 



06 Proceedings of the Royal Society of Edinburgh. [Sess. 



5 -6k 



4-5 



3-4k 






sl 


\ 

r 

N Y 


1 

sl 


' x 

+t?r>b. ^ 

< 


7^"* 1 

\ 



s of isobars and isotherms 
£ 1 J 1° — \Ktlomtbss 



scale, of wind velocity 

9 20 3 ,° 

J I 



7/ieCeo per second 



2-3i 






1-2 



0-1 




Fig. 4. — Pilot balloon sounding, April 29, 1908. North-west wind over south- 
west : characteristic of an advancing depression. 

The arrow shows the direction and velocity of the wind ; the full line, the position of 
isobar next above that which passes through the station. The dotted line through the 0 
shows the isotherm passing through the station ; the parallel dotted line, the isotherm 
for one degree higher than that of the station. 



107 



1913-14.] Principia Atmospherica. 

a sudden change of wind between 1100 and 1500 metres height from a 
reasonably steady wind from nearly due south into one almost as steady 
from due north, the change being accomplished within half a kilometre. 
The analysis in this case shows for the layer between 500 and 1100 metres 
a temperature distribution in isotherms nearly north and south with the 
warmer air on the east, and above 1500 metres an entirely different dis- 
tribution with isotherms nearly east and west, and cold to the northward. 
The intermediate layer, 400 kilometres thick, showed a very rapid increase 
of temperature to the west — as much as 7° C. per hundred kilometres. 

The complete arrest of the northerly current and production of a calm 
by the annihilation of the gradient between 1100 and 1500 metres is very 
remarkable, but nevertheless a real fact. The accompanying temperature 
difference is probably due to a strong temperature “ inversion ” at a height 
of about 1500 metres at the place of observation and of 1100 metres at a 
place 100 kilometres distant to the west. On that occasion it lasted for 
some time, as it was found an hour afterwards by a second balloon ; but it 
must be remembered that it was a region of no velocity, and therefore the 
relatively warm and cold airs were not moving. In order to get them 
away, either convection must take place or a gradient must be created. 



Proposition 6 . — The General Circulation of the Atmosphere in the 
Northern Hemisphere. 

The reasoning in this proposition is more general in form than that of 
the foregoing propositions. The extension of our knowledge tends more and 
more to strengthen the conclusion that the proximate cause of the varia- 
tions of pressure in the region of the British Isles must be looked for in the 
layer at a height of about 7 to 9 kilometres ; it is the layer of maximum 
wind- velocity just under the stratosphere, and it is also the layer within 
which must be located a rapid transition of slope of temperature. Below it, 
as set out in Lemma I., the slope of temperature follows the slope of 
pressure ; above it, the slope is in the opposite sense. The mechanism by 
which the changes of pressure are produced is unknown ; but this much is 
apparently true, that within the layer referred to, the relation between the 
pressure and temperature of the air at two places on the same level is that 
of adiabatic expansion. Above the critical layer where this relation holds, 
the air in the high-pressure area is “ too cold,” and below it, for 5 or 6 kilo- 
metres at least, it is “too warm.”* We may suppose that air becomes “too 
warm ’* by the dynamical warming of downward convection, and, perhaps, also 
* See Journal Scottish Met. Soc., 1913, loc. cit. 



108 Proceedings of the Royal Society of Edinburgh. [Sess. 



that it becomes “ too cold ” by piling np under the stratosphere and readjust- 
ment of the several layers within the stratosphere, so that pressure on the 
sample which causes the bulging is reduced, while that over the surrounding 
regions is increased.* Radiation is left out of account — whether rightly or 
wrongly, it is not possible at this stage to say. 

The motion of the critical layer is on the average from west to east, but 
not invariably so, and apparently the temperature-relations which have 
been described are not dependent upon wind direction. Other phenomena, 
so far as they have been observed, seem to indicate a similar symmetry, 
but there is no sufficient evidence for supposing that the phenomena are 
necessarily centred locally. In fact, according to the distribution of isobars 
at 4 kilometres computed by Teisserenc de Bort (Lemma II.), the average 
motion does not differ much from a circulation round the pole which, once 
set up, might be persistent with little change if it was everywhere 
adjusted to the barometric gradient. The actual motion, however, certainly 
does change, and is, in fact, constantly changing. 

Let us consider the conditions of Teisserenc de Bort’s average isobars 
and the forces which are available to produce the perturbations of a 
supposed original circumpolar circulation indicated thereby. I have 
already remarked that, for such a circulation as that represented by 
Teisserenc de Bort, the isobars for 4 kilometres may fairly be accepted as 
applicable at 7 kilometres also, because the changes of pressure-difference 
between 4 kilometres and 7 kilometres are in ordinary circumstances very 
slight. 

Taking the average map for January, it will be noticed that the 
isobars at 4 kilometres are clearly not circles round the pole. If they 
were so, a steady circulation would be a natural conclusion. It has been 
already postulated in Lemma II. that they are in reality indented ovals or 
approximate figures-of -eight with the lobes over the Asiatic and American 
continents and the inward bends over the two oceans. I purpose consider- 
ing first the effect of convection as a possible cause of the deviation from 
the circular shape. The shape which we have to explain is exactly 
opposite of that which is often shown on synchronous charts of the 
distribution of pressure at the surface of the Northern hemisphere in 
winter, and which has “ highs ” over the continents and “ lows ” over the 
oceans. I remark in the first place that, to derive the figure-of-eight shape 
from the circular shape, one cannot rely simply upon the nutation of a 
west-to-east circulation round the pole ; one must superpose either a pair of 

* See a note on the Perturbations of the Stratosphere in Publication 202 of the 
Meteorological Office. 



1913-14.] Principia Atmospherica. 109 

anticyclonic systems, elongated north or south, over the oceans, or a pair 
of cyclonic systems over the continents, of which we can at present only 
determine the southern portions ; or we might arrive at the actual shapes 
by adjustments of both kinds. If we assumed positions for the original 
circular isobars, it would be a simple matter to give numerical values of 
the superposed anticyclones or cyclones. But the circumpolar circular 
isobars are hypothetical, and, at the present stage, the numerical work 
indicated would be unremunerative. Let us assume, however, such an 
initial circumpolar system, and consider the physical forces which would 
disturb its motion. 

The only force immediately at hand is that of gravity, due indirectly 
to the cooling of the surface air on the land and frozen sea in the arctic 
night operating in accordance with Law 3, the law of convection. This 
may produce a real effect of some magnitude on land-slopes. It is not, 
I think, necessarily effective over level surfaces, because there is no slope 
down which the cooled air can flow. 

I have always hesitated about the common explanation of the trade- 
winds and other well-known phenomena based upon the reverse process of 
surface-heating. Surface-heating and surface-cooling necessarily produce 
a certain amount of expansion and contraction, but not necessarily any 
continuous convection current. Convection requires the juxtaposition of 
warm air and cold air, and, if the region is big enough, the result of 
surface-heating may easily give rise to a heated volume of air surrounded 
by isobars and air-currents that prevent any continuous process of general 
convection. Local convection there would be, but that need only extend 
high enough up to take up the day’s heat. All the main air-currents of 
the globe have pressure-distributions to guide them. They cannot usefully 
be called convection currents. 

So, if we had, say, a million square miles of level ice round the pole, 
I cannot see that the cooling of that area need produce any considerable 
effect upon the distribution of pressure ; but if the cooling takes place on 
slopes, we at once get the force of gravity to help, and one can no more 
suppose the downward flow of the air to be stopped than the flow of a 
river to be permanently arrested. Hence there must be in winter a 
continual flow of air off the great land-areas of the Northern hemisphere 
if they have any slope. The air-fall off Greenland, for example, must be 
enormous. Every description by explorers in the Antarctic seems to 
support the suggestion of a great cold-air cascade from the Antarctic 
continent. How much flows, and where it flows to, I cannot say ; ulti- 
mately it must find its way to warmer latitudes by some route or other ; 



110 Proceedings of the Boyal Society of Edinburgh. [Sess. 

but these air-flows must be a real cause of alteration in the distribution of 
pressure, and it is to the land-slopes which are losing heat that we may 
trace an indubitable influence, and therefore a disturbance of the uniformity 
of circulation. Apart from compensation, a flow-off of 1 metre thickness 
of air would mean a reduction of pressure by 0*1 millibar.* 

Similar phenomena must of course happen locally, and they are well 
known in mountainous regions, though we can hardly expect the smaller 
local examples to show much effect in the distribution of pressure over 
the globe. 

But we may assume that cold land-slopes in winter are the cause of a 
constant abstraction of air from the lowest layers of the atmosphere in 
those regions. The cold air flows away by gravity, and since the surface 
pressure is apparently still maintained, the efforts to redress the loss of air 
have to be carried out in the upper atmosphere and in accordance with its 
laws ; consequently we should expect to find a cyclonic circulation in the 
level in which the replacement is taking place. The cyclonic circulation 
may operate to prevent the pressure being made up overhead, but it cannot 
prevent the cold air from flowing downhill unless the reduction of pressure 
is enough to reduce the density by as much as the low temperature 
increases it, and this is a difficult task, for near sea-level it takes more 
than 3 millibars loss of pressure to make up for a single degree loss of 
temperature. 

Hence we may suppose that the constant drainage of the land-areas 
would result in the superposition of a cyclonic distribution at high level 
over them, and the continental lobes of Teisserenc de Bort’s isobars for the 
upper air may well be due to this cause. 

But the .cause is obviously a very variable one, depending upon the 
distribution of cloud and other circumstances. Statistically, its effect upon 
the circulation of the upper air is to exaggerate the pressure gradient for 
westerly winds over the temperate zones of the continents, and to diminish 
the gradient northward. Thereby we introduce into the circulation local 
accentuation of current, which must be disposed of by some dynamical 
process. 

* The facts which are here represented are sometimes taken as indicating the formation 
of anticyclones over the Arctic and Antarctic land-areas. When those areas are represented 
by plateaus 10,000 or 15,000 feet in height, the surface anticyclone may become merely a 
hypothetical construction supposed to occupy the space which is really occupied by land 
and not by air at all. To a considerable extent the great Asiatic and American anticyclones 
depend upon the reduction of observations to sea-level under conditions which can have no 
real existence. The mountain slope might possibly operate, in the maintenance of a 
cyclonic circulation in the upper air, much like the hole in the bottom of a basin, and the 
actual land-surface at the high level might therefore be a region of cyclonic circulation. 



Ill 



1913-14.] Principia Atmospherica. 

The next step in the consideration rests upon the fact that by superpos- 
ing a cyclonic depression upon the circumpolar circulation we displace a 
part of that circulation to the southward and reduce the northern part. 
Taking the case of Teisserenc de Bort’s map for January, the westerly run 
of isobars over America and Asia is about 10° to 20° of latitude lower than 
over the oceans, and these two positions of westerly circulation have to be 
connected by isobars which cross the parallels of latitude, and therefore 
have a south-to-north and a north-to-south component respectively. There- 
fore, they can only be maintained persistently under the conditions set out 
in Proposition 1. Now, it has been shown in the discussion of Proposition 1 
that permanence of a quasi-steady character might be realised in the case 
of an anticyclonic ridge having a south-to-north current on its western side, 
and vice versa, provided that momentum was being taken out of the 
westerly circulation in order to provide a slight eastward deviation from the 
isobars setting to the north. Such a case would be fairly represented by the 
deviation from circular isobars shown over the oceans on Teisserenc de Bort’s 
map for January, and hence the form of those isobars may be arrived at by 
the influence of a steady flow-off of air down the land-slope of the Arctic 
regions and the steady deviation of the wind from the direction of the 
south-west to north-west isobars on the western sides of the oceans in con- 
sequence of the momentum of the westerly circulation. 

Meanwhile, what happens to the cold air which has run off the land- 
areas ? That has to be steered about by the distribution of pressure in the 
upper air as modified by any special peculiarities of temperature in the 
lower regions, and all sorts of complications may arise from this cause. So 
far as it goes, its density tends to set up high pressure over the regions 
which it covers, and so to make a slope of pressure southward and cause 
easterly winds on its southern side. Whenever in a mass of air tempera- 
ture-fall is in the opposite direction to pressure-fall, great change in the 
horizontal distribution of pressure underneath is the result, and many of 
our local variations of pressure may fairly be attributed to the reactions 
which these cold masses of air offer to the attempt (in the end futile) on 
the part of the upper air to steer them round the pole from west to east. 
By their eastward motion these masses of cold air are always reminding us 
that if left to themselves, without the overpowering guidance of the 
pressure-distribution of the upper air, they would form a circulation round 
the pole in opposition to the circulation of the upper air, with which they 
are in perpetual conflict. 



112 



Proceedings of the Royal Society of Edinburgh. [Sess. 



Turbulent Motion. 

In the study which has been the subject of the foregoing pages we 
have always considered the motion of the air to he regulated by a dis- 
tribution of pressure balanced by the rotation of the earth, except in regard 
to the surface layer and one other suggested exception when the momentum 
of the general westerly circulation was invoked. It should here be noted 
that by this limitation to what may perhaps be called “ great circle motion,” 
we are considering almost exclusively the circulation above that half of 
the earth’s surface which is north of the northern tropic and south of the 
southern one. There is another section of meteorology which has to deal 
particularly with the region between the tropics where the beginnings of 
tropical revolving storms are to he found. These storms, which have 
a diameter of some hundred miles or more, as well as the tornadoes 
which have a diameter of perhaps a quarter of a mile, belong to the 
subject of turbulent motion, with which the eddies and whirls that are 
produced by obstacles on the surface of the ground are also associated. All 
these phenomena of turbulent motion, important as they sometimes are in 
real life and death, must be treated in a manner different from that of the 
present communication. 



(Issued separately March 23, 1914.) 



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MODEL INDEX. 

Schafer, E. A. — On the Existence within the Liver Cells of Channels which can be directly 
injected from the Blood-vessels. Proc. Roy. Soc. Edin., vol. , 1902, pp. 

Cells, Liver, — Intra-cellular Canaliculi in. 

E. A. Schafer. Proc. Roy. Soc. Edin., vol. 

Liver, — Injection within Cells of. 

E. A. Schafer. Proc. Roy. Soc. Edin., vol. 



, 1902, pp. 
, 1902, pp. 



IV 



CONTENTS. 



NO. PAGE 

VII. The Axial Inclination of Curves of Thermoelectric Force: a 
Case from the Thermoelectrics of Strained Wires. By 
John M‘Whan, M.A., Ph.D., Lecturer in Mathematics in 
the University of Glasgow. ( Communicated by Professor 
Andrew Gray, LL.D., F.R.S.), . . . .64 

(Issued separately March 20, 1914.) 

VIII. The Path of a Ray of Light in a Rotating Homogeneous and 
Isotropic Solid. By E. M. Anderson, M.A., B.Sc. ( Com- 
municated by The General Secretary), . . .69 

(. Issued separately March 20, 1914.) 

IX. Principia Atmospherica : a Study of the Circulation of 

the Atmosphere. An Address delivered at the request of 
the Council before the Royal Society of Edinburgh, on 1st 
December 1913. By W. N. Shaw, LL.D., Sc.D., F.R.S., 
Director of the Meteorological Office, Reader in Meteorology 
in the University of London, . . . . .77 

{Issued separately March 23, 1914.) 



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Part IX.] VOL. XXXIV. [Pp. 113-208. 



CONTENTS. 

NO. PAGE 

X. Enzymatic Peptolysis in Germinating Seeds. By Dorothy 
Court, B.Sc., Carnegie Research Fellow. Communicated 
by Professor E. Westergaard, . . * . . 113 

( Issued separately March 26, 1914.) 

XI. A Study of the Curvatures of the Tasmanian Aboriginal 
Cranium. By L. W. G. Buchner, Victorian Government 
Research Scholar in the Anthropology Department of the 
University of Melbourne. Communicated by Professor 
R. J. A. Berry. (With Three Folding Tables), . .128 

(Issued separately April 28, 1914.) 

XII. The Place in Nature of the Tasmanian Aboriginal as deduced 

from a Study of his Calvaria. — Part II. His Relation to 
the Australian Aboriginal. By Richard J. A. Berry, M.D. 

Edin., Professor of Anatomy in the University of Melbourne; 
and A. W. D. Robertson, M.D. Melb., Government Research 
Scholar in the Anatomy Department of the University of 
Melbourne. (With One Folding Table), . . 144 

(Issued separately April 29, 1914.) 

XIII. A Chemical Examination of the Organic Matter in Oil Shales. 

By John B. Robertson, M.A., B.Sc., Carnegie Scholar. 
Communicated by Dr J. S. Flett, F.R.S., . . 190 

(Issued separately July 15, 1914.) 

[ Continued on page iv of Cover. 

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[Continued on page iii of Cover. 



1913-14.] Enzymatic Peptolysis in Germinating Seeds. 



113 



X. — Enzymatic Peptolysis in Germinating Seeds. By Dorothy 
Court, B.Sc., Carnegie Research Fellow. Communicated by 
Professor E. Westergaard. 

(Read December 15, 1913. Revised MS. received February 10, 1914.) 

In a previous paper ( Proc . Roy. Soc. Edin., vol. xxxi. p. 342) a method was 
described for measuring small degrees of enzymatic peptolysis, and in a 
subsequent paper {Proc. Roy. Soc. Edin., vol. xxxii. p. 251) the conditions 
were dealt with under which such experiments could be carried out with 
the greatest possible guarantee of sterility combined with the least inter- 
ference with the reaction. 

The intention was to employ these methods for the purpose of pursuing 
the main object of research — the activation of zymogens in germinating 
seeds — and it was accordingly decided to carry through a series of ex- 
periments on germinating barley. This material was selected on account 
of the readiness with which it may be obtained. 

The presence of proteolytic and peptolytic enzymes in germinating 
barley has been previously described by Weis {C. R. Carlsberg Lab., vol. v. 
p. 127), Vines {Ann. Bot., xvi. 1), and Abderhalden and Dammhahn {Zeit- 
schrift fur physiol. Chemie, lvii.). 

Weis, working with a watery extract of crushed germinated barley, 
found evidence of proteolytic as well as peptolytic activity, and it was 
therefore decided to use a similar extract in some preliminary experiments. 
For this purpose 900 grms. of material were crushed in a mincing 
machine and extracted with 700 c.c. chloroform w r ater for twenty hours. 
The liquid was expressed in a hand-press, filtered, neutralised with sodium 
bicarbonate, and divided into three portions. One of these was made 
slightly acid ( = '2 per cent, lactic acid), one was made alkaline ( = T per 
cent. NaHCo 3 ), and one remained neutral. One gramme of Pepton Roche 
was dissolved in 10 c.c. of each of these preparations, T c.c. chloroform 
added, and the mixture incubated at 37°. It was somewhat surprising to 
find that though the digestion was carried on for several days no deposit 
of tyrosin was obtained. 

At the same time another experiment was carried out with the same 
material for the purpose of determining the relative activities of the 

embryo and endosperm of the seed. The embryos were carefully dissected 

vol. xxxiv. 8 



114 



Proceedings of the Royal Society of Edinburgh. [Sess. 

out, ground with sand and a 1 per cent, solution of Pepton Roche, filtered, 
and the filtrates digested at 37° C., 1 per cent, chloroform being added. 
This procedure was also followed out with the residues and with a sample 
of the whole seed. In each of these cases, as before, a number of the 
digestions were allowed to remain neutral, while others were acidified and 
made alkaline respectively. An entirely negative result was obtained from 
these experiments also. 

The experiments described above were repeated several times with 
different samples of material, the digestions were carried out within a wide 
temperature range (15°, 25°, 37°, 50°), and the period of incubation was 
extended to as much as three weeks. It thus became obvious that an 
invariable negative result could not be due to any accident, but to the 
absence of a peptase capable of splitting off tyrosin from Pepton Roche. 
It was therefore decided to carry through a final experiment in order 
to investigate the matter fully. 

For this purpose a sample of germinating barley was ground up in a 
mincer, extracted for twenty-four hours with chloroform water, and pressed 
in a hand-press. The liquid was freed from suspended particles by means 
of a centrifuge. This extract will, in the following pages, be referred to as 
Extract A. 

The residue from the press was then ground with sand and kieselguhr, 
with the addition of a little water, in the Buchner mortar, and then subjected 
to a pressure of 300 kg. per sq. cm. in the Buchner hydraulic press. The 
liquid obtained in this way, and freed from solid matter as before, will be 
referred to as Extract B. 

Twelve flasks were made up, each containing 5 c.c. 20 per cent. Pepton 
Roche solution and 5 c.c. Extract A, while another twelve were similarly 
prepared with Extract B, T c.c. chloroform being added to each as anti- 
septic. Three of each series were digested at each of the following 
temperatures — 15°, 25°, 37°, 50°. At the same time a similar number of 
flasks containing 5 c.c. 10 per cent. Pepton Witte solution instead of the 
Pepton Roche were placed at the same temperatures, a series of controls 
being prepared for the latter experiment by precipitating the material at 
once with excess of tannic acid. The digestions were examined from day 
to day, and whenever a deposit was found it was filtered off and the 
identity of the tyrosin established by means of Morner’s reaction, the corre- 
sponding Pepton Witte digestions being precipitated with tannic acid at the 
same time. 

The first deposits of tyrosin were produced within six days in the diges- 
tions containing Extract B, at 25° and 37° respectively; the next ones 



19 13- L 4.] Enzymatic Peptolysis in Germinating Seeds. 115 

being formed after a period of fourteen days in the Extract B digestions at 
15°. The remainder of the digestions gave negative results after three weeks’ 
incubation, when the experiment was discontinued and the Pepton Witte 
digestions precipitated. The filtrates from these were used in the manner 
described by Weis (l.c.) for determining the degree of peptolysis which 
had taken place during incubation, expressed in terms of cubic centimetres 
of N/10 alkali, this latter figure representing the ammonia formed during 
the determination of the nitrogen contained in 5 c.c. of the filtrate, by 
Kjeldahl’s method. 

The results of the experiment may be seen in the following tables 



Extract A, with 



1. Pepton Witte. 



Temperature 

of 

Digestion. 


Titrations. 


Average. 


Control. 


Difference 
(indicating enzyme 
action). 


15° 


1. 2. 
8*9, 9T, 


3. 

9*5 


9T6 


14*9 


5-74 


25° 


6-0, 5-5, 


5-6 


5 - 7 


15-3 


9-6 


37° 


6T, 6’1, 


— 


6T 


15*3 


9*2 


50° 


8-3, 8-4, 


— 


8*35 


15-5 


7'15 



2. Pepton Roche. 

The whole of this series of digestions gave negative results. 



Extract B, with 
1. Pepton Witte. 


Temperature 








Difference 


of 


Titrations. 


Average. 


Control. 


(indicating enzyme 


Digestion. 








action). 




1. 2. 3. 








15° 


13*25, 12-55, 12-55 


12-78 


15-8 


3-0 


25° 


7-7, 7-4, 7-1 


7-4 


16-8 


9-4 


37° 


7-2, 8-2, 6-65 


7-35 


16-85 


95 


50° 


10-15, 9-0, 


9-55 


16-0 


6-45 




2. 


Pepton Roche. 





15°. Positive result observed after fourteen days. 
25°. Strongly positive result within six days. 

37°. Positive result also within six days. 

50°. Negative result. 



116 Proceedings of the Royal Society of Edinburgh. [Sess. 

The total result of the experiment may, for the sake of comparison, be 
expressed as follows : — 



Results of Peptolysis. 



Temperature. 


Pepton 


Witte. 


Pepton Roche. 


A. 


B. 


A. 


B. 


15° 


5*74 


3-0 


Negative. 


14 days. 


25° 


9*6 


9-4 




6 „ 


37° 


9*2 


95 




6 „ 


50° 


7T5 


6*45 




Negative. 



These results seem to indicate the presence in germinating barley of 
two different peptolytic enzymes, one of which can be readily extracted 
with water, while the other is apparently of the nature of an endo-enzyme 
and can only be obtained by destroying the cells of the seed tissues. The 
existence of these two enzymes is further indicated by the fact that their 
temperature curves differ materially. The optimum temperature for both 
seems to be between 25° and 37°. At 50°, however, while the hydrolysis of 
Pepton Witte proceeds vigorously, being considerably more marked than 
at 15°, the action on Pepton Roche seems to be inhibited, since no separation 
of tyrosin has ever been observed at this temperature. On the other hand, 
a slow but quite distinct action takes place at 15°. 

The inhibition of the Pepton Roche digestion at 50° was further 
accidentally demonstrated in this way. A number of digestions which had 
been incubated at 15° and 50° for six days, with a negative result, were 
put aside and overlooked for a couple of weeks. It was then found that 
those which had been at 15° for the whole period gave a distinct deposit of 
tyrosin, while those which had previously been exposed to a temperature 
of 50° showed no such deposit. Apparently the Pepton Roche digestion 
is not only prevented at 50° but the activity completely destroyed, while, 
as has been previously demonstrated, the hydrolysis of Pepton Witte pro- 
ceeds vigorously at this temperature. 

The digestions were all examined for the presence of moulds or bacteria, 
partly by microscopic examination and partly by adding a drop of the 
material to sterile meat-extract gelatine and incubating at 20°. This 
examination invariably showed the absence of any development of bacteria 
or fungi. In a few cases only, an isolated Penicillium spore seemed to 
have survived. 

For the sake of certainty on this point another experiment was devised. 
The barley was crushed, mixed with sand and kieselguhr, and ground in 



117 



1913-14.] Enzymatic Peptolysis in Germinating Seeds. 

the Buchner mortar. A suitable quantity of Pepton Roche solution was 
then added and the resulting mass subjected to a pressure of 300 kg. per 
sq. cm. in the Buchner press. The expressed liquid was freed from sus- 
pended particles by means of the centrifuge, and then passed through a 
Chamberland filter into sterilised Pasteur flasks, which were afterwards 
placed at the same temperatures as were employed before. 

The results obtained from this experiment were similar to those 
obtained before with regard to the separation of tyrosin — a strongly 
marked reaction at 25° and 37°, a less marked but distinct reaction at 15°, 
and no reaction at 50°. 

Part of the contents of the flask which had been incubated at 25°, and 
which had given the heaviest deposit of tyrosin, were transferred to a 
Pasteur flask containing sterilised glucose-Pepton Witte solution and further 
incubated at 25°. The contents of the flask were found to remain sterile 
throughout the whole period of incubation, which extended over several 
weeks, proving conclusively that the peptolysis was not due to any 
development of micro-organisms. 

The presence in germinating barley of two distinctly different peptases 
having be,en thus established, the next step in the main research became 
that of ascertaining at what period the activation of the above-mentioned 
peptases takes place, in order that the conditions influencing the activation 
might be finally studied in detail. 

For the purpose of elucidating this point, the peptolytic activity was 
determined from time to time in a sample of barley during germination 
and the results confirmed, firstly, with another quantity of the same sample, 
and secondly, by repeating and extending the experiment with a different 
sample. 

The examination was in each case commenced with the ungerminated 
barley, and was continued in the first two instances for seventeen days, in 
the last instance for twenty-nine days. The germination took place under 
the conditions usually observed in the preparation of malt, and the samples 
were examined at intervals of from two to four days. 

The water content was determined in every sample withdrawn for 
examination, by placing 5 grms. of the ground material in a weighing 
bottle, covering it with absolute alcohol, and drying it in a hot- water oven 
for twenty-four hours. 

500 grms. of barley were disintegrated in a mincing machine and 
ground in a Buchner mortar with 500 grms. of sand and a suitable quantity 
of water to make a firm paste. This was placed in a Buchner press and 
subjected to a pressure of 350 kg. per sq. cm. for about one hour, when no 



118 



Proceedings of the Royal Society of Edinburgh. [Sess. 

more liquid could be expressed, and the extract was finally made up with 
distilled water to 350 c.c. 

The liquid was freed from suspended particles by means of a centrifuge, 
and was thereafter divided into two portions, one of which was mixed with 
a solution of Pepton Witte in such quantities as to give a concentration of 
2 per cent, peptone, whilst 10 per cent, of Pepton Roche was dissolved in 
the other. 

The liquids were then placed, in quantities of 10 c.c., in a number of 
small bottles, each of which received in addition T c.c. of chloroform. 
Excess of tannic acid and a trace of sodium acetate were added to half of 
those bottles containing Pepton Witte, while the remainder of these and all 
those containing Pepton Roche were placed in an incubator at 35° C. 

The Pepton Witte digestions were withdrawn after forty-eight hours’ 
incubation, precipitated with tannic acid and sodium acetate, and, along 
with the controls, which were precipitated before digestion, filtered and * 
used for determining the amount of nitrogen contained in 5 c.c. of the 
filtrate, Kjeldahl’s method being employed. 

The increase in nitrogen, expressed in cubic centimetres of N/10 
alkali, was, as before, taken as an indication of the amount of peptolytic 
activity during digestion. 

This difference was, in all cases where ungerminated barley was em- 
ployed, within the limits of experimental error, and the resting seed of 
barley may therefore be regarded as containing only in extremely small 
quantities, if at all, a peptase capable of catalysing the hydrolysis of the 
polypeptids contained in Pepton Witte. 

A peptase of this nature was, however, found to be rapidly produced 
during germination, as will be seen below. 

In the following tables, the first column shows the number of days from 
the time when the barley was steeped in water to the time when the 
sample was withdrawn for examination, while the second column gives the 
degree of peptolytic activity expressed in cubic centimetres of N/10 acid 
neutralised by the ammonia formed during the Kjeldahl process, and in 
each case corrected for the amount of moisture contained in the sample. 

The Pepton Roche digestions were examined from day to day, and a 
note was made of the minimum number of days within which a deposit of 
tyrosin was formed. 

Although there is no experimental evidence to show that under the 
conditions of the experiment, and especially considering its duration, the 
time required to produce a precipitate is inversely proportional to the 
degree of activity, it is nevertheless obvious that, the greater the peptolytic 



1913-14.] Enzymatic Peptolysis in Germinating Seeds. 119 

activity, the more rapidly will the tyrosin be precipitated, and vice versa. 
The figures obtained in this way are therefore sufficient indication of the 
degree of activity, provided that they are expressed in a manner capable 
of direct comparison, and they are therefore, in the following tables, 
expressed in terms of a unit which, under the conditions of the experiment, 
would produce the first indication of tyrosin in 100 days. The amount of 
moisture contained in the samples has here, as in the case of the Pepton 
Witte digestions, been taken into consideration, the figures shown being 
calculated for dry material. These results are given in the third column. 



Table I. 


Number 
of days. 


Pepton Witte. 


Pepton Roche. 


4 j in water 


o-oo 

4T3 


2-80 

8-56 


6 


7-59 


8-25 


8 


11-60 


20-45 


10 


11-60 


37-40 


13 


11-20 


45-30 


15 


11-0 


58-70 


17 


11-32 


34-60 


Table 11. 


0\ • , 


o-oo 


2-45 


4 > m water 


6'24 


7-88 


6 


9-16 


12-40 


10 


11-50 


24-90 


12 


12-05 


24-40 


13 


14-60 


43-35 


15 


13-27 


34-60 


17 


13-48 


24-06 


Table III. 


01 • 

. m water 

4 f 


o-oo 

4-49 


2-20 

6-30 


6 


7-83 


7-40 


8 


9-77 


16-76 


10 


9-83 


24-30 


12 


9-81 


35-00 


15 


14-10 


42-50 


17 


12-75 


75-40 


19 


1215 


41-20 


20 


10-55 


3940 


22 


11-22 


38-95 


24 


11-12 


Lost. 


26 


13-72 


31-57 


29 


12-84 


25-50 



120 Proceedings of the Royal Society of Edinburgh. [Sess. 

It is obvious from the whole nature of the experiment, and from the 
manner in which the different samples were obtained, that a certain amount 
of irregularity must be expected in the results. Such fluctuations, however, 
have not been found to be nearly so serious as was anticipated. The fact 
that the maximum degree of activity is reached somewhat later in the third 
than in the first and second experiments is easily explained by the fact that 
an entirely different variety of barley was used, while the other irregularities 
are so small that they cannot obscure the evidence of the experiments, to 
the effect that, of the two forms of activity, the one rises sharply from 
nothing in the ungerminated seed till it reaches its maximum, after which 
it remains fairly constant during the remainder of the experiment. On the 
other hand, the activity in the second case rises comparatively slowly from 
slightly above zero in the ungerminated seed till it reaches its maximum a 
few days later than in the former case, after which it rapidly falls again. 

The presence of both of these forms of activity in germinating barley 
having been thus demonstrated, it seemed desirable to investigate the 
existence of similar enzymes in material of widely different origin. For 
this purpose the strongly proteolytic and peptolytic enzyme, Bromelin, 
contained in the juice of the fruit of Ananassa sativa, was selected. In 
order to make the experiments more complete, it was decided to carry out 
parallel digestions, using as substrate in one case the alcohol-soluble 
protein of wheat, and in the other a solution of Pepton Witte. 

The digestions were carried out partly in presence of the natural acidity 
of the juice, partly with a juice that had been neutralised, and partly with 
a portion made slightly alkaline with sodium bicarbonate. In each case 
5 c.c. of the juice was employed, and three digestions were carried out with 
each substrate and each reaction. 

The following series of digestions were accordingly prepared : — 

(a) 2 grms. protein + 5 c.c. water + 5 c.c. juice. 

(b) 5 c.c. 4 per cent. Pepton Witte solution + 5 c.c. juice. 

( c ) 5 c.c. 10 per cent. Pepton Roche solution -f 5 c.c. juice. 

As usual, half of the digestions (a) and ( b ) were precipitated before 
digestion with tannic acid ; the others, along with (c), being digested at 37°. 
After twenty-four hours (a) and ( b ) were withdrawn and precipitated, the 
nitrogen contents of the filtrates estimated, and the amount of peptolysis ex- 
pressed as before. The results are given in the following table, and show that 
a very strong proteolysis and peptolysis had taken place. The corresponding 
Pepton Roche digestions, however, showed no deposit of tyrosin, even after 
three weeks’ incubation, and it is therefore safe to conclude that bromelin 
does not decompose this polypeptid. Whether an enzyme capable of doing 



1913-14.] Enzymatic Peptolysis in Germinating Seeds. 121 



so is present in the cells of the fruit, and might be extracted by the 
Buchner method, was not determined at the time. 



Juice of An an ass a sativa on 
1. Protein. 


Reaction of 
Medium. 


Titrations, 
[c.c. N/10 NaOH] 


Average. 


Control. 


Difference 

(indicating 

enzyme 

action). 


Acid 


2-5, 2-55, — 


2*52 


8-5 


60 


Neutral .... 


6*6, 7-0, 57 


6'46 


8T 


1-64 


Alkaline .... 


6-8, 6-6, 5*7 


6-4 


8-6 


2-2 


2. Pepton Witte. 


Acid ..... 


2*4, 2'4, — 


2-4 


5-6 


32 


Neutral .... 


4-4, 4-1, — 


4*25 


5-9 


1-65 


Alkaline .... 


5-2, 5-5, 6-0 


5-56 


6-0 


•44 




3. Pepton Roche. 






The whole of this series gave negative results. 





About the same time a number of fungi were gathered, ground to pulp 
with sand in a mortar, and the juice pressed out in the hand -press. The 
preparations thus obtained were used in a similar series of experiments, 
the only difference being that the digestions were in this case confined to 
the natural reaction of the extracts, in all cases slightly acid. 

The results were as follows 



Fungus. 


Protein Digestions. 


Pepton Witte Digestions. 


Titrations. 


Aver- 

age. 


Con- 

trol. 


Diff. 


Titrations. 


Aver- 

age. 


1 n 

Con- 

trol. 


Diff. 


Lycoperdon gemmatum 


9-2, 


9-35, 


9T5 


9-23 


9-45 


•22 


5*6, 5-3, 5-2 


5-36 


8-4 


3*0 


Hyphaloma capnoides . 


8-75, 


8-95, 


8-85 


8-85 


9-5 


•65 


5-8, 5-9, 5-7 


5-8 


8-5 


2-7 


Hyphaloma trichaloma 


9-15, 


9-0, 


9-2 


9:12 


9-4 


•28 


6-1, 61, 6T 


6T 


8-4 


23 


Russula emetica . 


9'1, 


9-2, 


9T 


9T3 


9*3 


T7 


6-8, 6-7 — 


6-75 


8-6 


1*85 


Boletus badens 


8-9, 


8*7, 


8-9 


8'83 


93 


•5 


5 3, 5*5, 5-4 


5*4 


8-3 


2-9 


Laccaria laccata . 


10*0, 


9-85, 


9-6 


9-8 


9-85 


•05 


6-9, 6*7, 7-0 


6-86 


8-8 


1-94 


Hydnum repandum 


.9-3, 


9*1, 


9-2 


9-2 


93 


T 


7-0, 6-6, 6-4 


6-6 


8-7 


2T 


Amanita rubescens 


7-0, 


7-6, 


7*5 


736 


8-9 


1-54 


3-9, 4-0, 4T5 


4-0 


7-7 


3*7 


Amentopsis strangulata 


7*7, 


7-65 


8-0 


7-78 


8-9 


1-12 


4-7, 4-7, 4-5 


4-63 


7‘8 


317 



Pepton Roche. 

The whole of these gave negative results. 



122 



Proceedings of the Royal Society of Edinburgh. [Sess. 

From this it will be seen that a distinct peptolytic action is found in all 
cases on Pep ton Witte, and a slight action in some cases on the protein. 
The result of the Pepton Roche experiment remained negative after several 
weeks. Neither was it determined in this case, however, if the cell 
contents obtainable by the Buchner process would be capable of hydrolys- 
ing Pepton Roche, as the small quantities of the material available did 
not allow of the use of this method. It would, however, seem probable 
that a considerable proportion of the cell contents must have been liberated 
during the grinding, since sand was employed, and since the tissue of these 
fungi is by no means difficult to disintegrate. It would therefore seem 
almost safe to assume the entire absence of this enzyme in all the cases 
in question. 

For further information, a series of experiments was carried out with 
the ordinary cultivated mushroom, which can be bought in quantities. The 
preparations were made as in the case of barley, Extract A being obtained 
by grinding in an ordinary mortar and expressing in a hand-press, while 
Extract B was obtained from the residue by the Buchner method. The 
following results were obtained : — 



Agaricus campestris. — Extract A. 


Substrate. 


Titrations. 


Average. 


Control. 


Difference. 


Protein .... 
Pepton Witte 
Pepton Roche 


5-3, 5-4, 5*3 
1-7, 1'9, 1*5 
Positive 


5*36 

P7 

result obtaine( 


6-8 

6*0 

1 within 24 ho 


1*44 

4-8 

urs. 


Extract B. 


Protein .... 
Pepton Witte 
Pepton Roche 


8-8, 9-2, 9T5 
6-8, 6*4, — 

Positive resull 


9-05 

6*6 

b obtained onh 


9-2 

73 

l after 7 days 5 


T5 

•7 

digestion. 



These results show at once the presence of a tyrosin-separating enzyme, 
and also that this, as well as the other forms present in this material, had 
been extracted in the first pressing, the amount remaining in the residue 
being doubtless removable by washing. To obtain confirmation of the 
presence of this enzyme in Agaricus, another quantity was ground with 
sand and kieselguhr and expressed in the Buchner press. Digestions similar 
to those just described were carried out with the following results : — 



1913-14.] Enzymatic Peptolysis in Germinating Seeds. 



123 



Agaricus campestris — Extract on 



Protein . 
Pepton Witte 
Pepton Roche 



Titrations. 


Average. 


Control. 


5-9, 6-0, 6T 


6-0 


7-3 


2-8, 2-3, 2-35 


2-5 


6-3 


Positive result- 


—marked. 



Difference. 



1-3 

3-8 



A number of experiments similar to those just described have also been 
carried out, using as material Saccharomyces cerevisice, Penicillium glaucum, 
Aspergillus niger. 

In the case of Saccharomyces cerevisice three experiments were 
carried out: — 

I. Washed and pressed yeast was extracted for twenty-four hours with 
chloroform water, and the filtered liquid allowed to act on the protein, 
Pepton Witte, and Pepton Roche as before, at 37° C., using the same concen- 
trations as in the previous experiments. Three digestions were carried 
out with each substrate, and in the case of the protein and Pepton Witte 
two controls were precipitated before digestion. 

The Pepton Roche digestions did not give any precipitate of tyrosin 
within three weeks, thus indicating the absence of this form of activity 
in the extract. The other digestions were all precipitated after twenty-four 
hours’ incubation and used for nitrogen determination in the usual manner, 
with the following results : — 





Titrations. 


Average. 


Control. 


Difference. 


Protein .... 


9-3, 9T, 9T5 


9T8 


9T0 


*08 


Pepton Witte 


7-9, 7-6, 7-8 


7*77 


8*5 


•27 



II. Washed and pressed yeast was ground with sand and kieselguhr in 
the Buchner mortar, the liquid expressed in the usual manner and freed 
from suspended particles by means of a centrifuge. Digestions similar to 
those described above were carried out, using 2 c.c. of the liquid in each 
case and adding distilled water to obtain the same concentrations of the 
substrate. 

All the Pepton Roche digestions gave a strong deposit of tyrosin within 
twenty-four hours. 

The other digestions were all precipitated after twenty-four hours’ incuba- 



124 Proceedings of the Royal Society of Edinburgh. [Sess. 

tion, and the nitrogen content determined in the usual way. The results 
were as follows : — 





Titrations. 


Average. 


Control. 


Difference. 


Protein .... 


87, 8*6, 8-5 


86 


9*3, 9T 


0-6 


Pepton Witte 


4T, 4T5, 4-2 


4-15 


8-0, 8-2 


3-95 



III. A watery extract was first obtained, as in the first experiment, and 
the residue subjected to the Buchner method process in order to obtain the 
cell contents. The same conditions were observed as in the previous experi- 
ments, with the difference that the digestions were carried out with Pepton 
Witte and Pepton Roche only and that four temperatures were employed, 
viz. 15°, 25°, 37°, 50°. 

The results will be seen from the following table : — 





Extract A, with Pepton 


Witte. 




Temperature. 


Titrations. 


Average. 


Control. 


Difference. 


15° 


7-9, 7-4, 8-2 


7-83 


7 '9 


•07 


25° 


8-3, 8-5, 7-9 


8*23 


8-5 


•27 


37° 


8-0, 8-0, 8-0 


8-00 


8-0 


•00 


50° 


7-9, 8-0, 8-0 


7-97 


8T 


T3 




Extract A, with Pepton 


Boche. 






All results were negative. 




Extract B, with Pepton Witte. 


15° 


6-0, 6*4, 5-9 


6T0 


7-60 


1-50 


25° 


2-35, 2-5, 2-8 


2-55 


7-60 


5 05 


37° 


2-4, 2-0, 


2-20 


7-50 


5*30 


50° 


3-6, 3-6, 33 


3-76 


7*40 


394 




Extract B, with Pepton 


Roche. 




15°, 


. Slight positive result within twenty-four hours. 


25°. 


Strong 


55 


55 




37°. 


55 55 


55 


>5 




50°. 


Negative result at the end of three weeks. 





In the case of Penicillium glaucum and Aspergillus niger, pure cultures 
were developed in sterilised 10 per cent, malt extract in large flasks at 
room temperature. After several weeks a large growth had taken place, 



125 



1913-14.] Enzymatic Peptolysis in Germinating Seeds. 

and all the cultures were in a state of fructification. As much as possible 
of the liquid was then poured off and discarded, while the liquid remaining 
amongst the mycelium was expressed by means of the hand-press. This 
was retained for experiment as Extract A. 

The mycelium was then ground in the usual way in the Buchner 
mortar and pressed in the Buchner press. In this way two liquids were 
obtained from each of the fungi — a medium, and a mycelium extract- 
Digestions were made as before with these preparations, using protein, 
Pepton Witte, and Pepton Roche as substrates. The results may be seen 
in the following tables : — 



Penicillium glaucum — Extract A (Hand-press Extract) on 




Titrations. 


Average. 


Control. 


Difference. 


1. Protein .... 


8-3, 8T5, 8T5 


8-2 


9-45 


1-25 


2. Pepton Witte 


8-4, 8-7, 8-2 


8-46 


8-9 


•44 


3. Pepton Roche 




All negative. 




Extract B (Buchner Extract) on 


1. Protein .... 


6-4, 7*0, 6-7 


6-7 


8-8 


2*1 


2. Pepton Witte 


4-8, 5*0, 5-2 


5-0 


8-6 


3-6 


3. Pepton Roche 




All negative. 





Aspergillus niger — Extract A on 





Titrations. 


Average. 


Control. 


Difference. 


1. Protein .... 


8-0, 7*0, 7-5 


7-5 


9*3 


1-8 


2. Pepton Witte 


6*2, 6*1, 6-0 


6T 


8-9 


2-8 


3. Pepton Roche 




Negative result. 




Extract B on 


1. Protein . 


6-75, 6-9, 6-3 


6-65 


8-3 


D65 


2. Pepton Witte 


2-2, 2-5, — 


2-35 


6-8 


4-45 



3. Pepton Roche 



In the apparently complete absence of the Pepton Roche hydrolysing 
activity in Penicillium glaucum, a striking contrast is shown with Asper- 
gillus. In view of the close relationship existing between these fungi, it 
was thought desirable to ascertain if Penicillium could be brought to 



126 



Proceedings of the Royal Society of Edinburgh. [Sess. 

produce this enzyme. A sterilised solution of sugar and Pepton Roche was 
made up and infected with a pure culture, and then incubated at 20° for 
several months. The development was, however, so small that it was 
quite impossible to carry out any examination of the mycelium, and no 
deposit of tyrosin appeared in the culture medium. 

The results obtained with the watery extracts of Saccharomyces are so 
slight that they must be regarded as being within the limits of experi- 
mental error. It is, however, possible that more active preparations could 
have been obtained by prolonged extraction or by addition of sodium 
chloride as suggested by Vines (Ann. Bot., vol. xviii. p. 289, 1904). The 
results are, however, in conformity with the statement made by that author, 
to the effect that a rapidly prepared watery extract of yeast has no proteoly- 
tic action, and with those of Geret and Hahn (Buchner, Die Zymasegdhrung , 
1903, p. 287) that the Buchner extract possesses a much stronger proteolytic 
action than that exhibited by the living yeast towards its substrate, and 
that the proteolytic and peptolytic activity is due to a cell enzyme. 

Whether this enzyme, as suggested by Geret and Hahn (l.c.), is of the 
nature of a tryptase has already been rendered doubtful by the works of 
Bokorny (Beihefte, Bot. Gentr., vol. xiii. p. 235, 1903), who suggested that an 
enzyme of the pepsin group is also present, and Vines (l.c.), who found 
evidence of the presence of an ereptase. 

In this connection, the results obtained with the Buchner extract 
(Extract B), which are shown in the preceding tables, are of interest. 

In the first place, it will be noticed that there is a strong peptolytic 
activity against Pepton Roche as well as against Pepton Witte. Secondly, 
the decomposition of Pepton Roche, as in the case of barley, is inhibited at 
50°, whereas the hydrolysis of Pepton Witte proceeds vigorously at that 
temperature. Thirdly, assuming the activity on Pepton Roche to be in- 
versely proportional to the time required for producing the first indication 
of tyrosin, this activity is, in the case of Saccharomyces, much more pro- 
nounced as compared with the action on Pepton Witte than in the case of 
barley, a fact which further supports the view of the non-identity of the 
two enzymes. Further, the proteolytic activity exhibited by the Buchner 
extract of Saccharomyces is very slight in comparison with the peptolytic 
activity, a fact which becomes even more striking when the results are 
compared with the corresponding figures obtained with Penicillium and 
Aspergillus. Finally, it would seem highly unlikely that the proteolysis 
and the peptolysis are catalysed by the same enzyme, as in that case the 
primary reaction would need to be accelerated in at least the same degree 
as the secondary one, which is obviously not the case. 



1913-14.] Enzymatic Peptolysis in Germinating Seeds. 127 

Whether the comparatively slight proteolytic activity observed in the 
present investigation in the Buchner extract of yeast, and previously 
described by other observers (Geret and Hahn, Vines, etc.), is due to a 
trypsin or a pepsin is uncertain ; but it is fairly evident that the peptolysis 
is almost entirely due to different agents, and it would further seem highly 
probable that these agents are similar to the two peptases found in ger- 
minating barley, if they are not identical with them. 



(Issued separately March 26 , 1914 .) 



128 



Proceedings of the Royal Society of Edinburgh. [Sess. 



XL— A Study of the Curvatures of the Tasmanian Aboriginal 
Cranium. By L. W. G. Buchner, Victorian Government Re- 
search Scholar in the Anthropology Department of the University 
of Melbourne. Communicated by Professor R. J. A. Berry. 
(With Three Folding Tables.) 

(MS. received December 9, 1912. Read January 19, 1914.) 

The extinction of the Tasmanian aboriginal in 1876 closed, for all practical 
purposes, the further scientific study of this ancient and highly interesting 
race, and it appeared almost certain that our knowledge of this people 
would remain dependent on the earlier works of those who were fortunate 
enough to have studied them during life, and on the few remains housed 
in such fortunate centres as London, Paris, Edinburgh, Oxford, and 
Cambridge. 

Fortunately, just at the moment when it seemed most improbable that any 
further specimens of Tasmanian crania would be discovered — the number 
known to be in existence up to 1909 having been given by Turner as 
seventy-nine, — Berry and Robertson published in the Proceedings of the 
Royal Society of Victoria (1) and the Anatomischer Anzeiger (2) an 
account of a further discovery of fifty-two. This discovery, important 
though it undoubtedly was, would not materially have greatly advanced 
Tasmanian craniology, had not the dioptrograph and diagraph just been 
invented. By the use of the former ingenious and accurate instrument, 
Berry and Robertson were enabled to record the whole of their fifty-two 
crania — forty of which were absolutely new to science — in such a way 
as to make any craniological investigations on these skulls available in 
any part of the world. 

The great importance of this method was immediately realised, amongst 
others, by Professor Sergi of Rome, who hastened to avail himself of this 
unexpected increase in the wealth of Tasmanian material available, in order 
to study anew the form of the Tasmanian skull by means of his own 
highly original modes of investigation. The results have been made 
available to us in his recently published “ Tasmanier und Australier, 
Hesperanthropus tasmanianus , spec.” (3). 

The publication of Berry and Robertson’s Atlas has also made it 
possible for any investigator to apply any of the recently introduced 
craniological and morphological methods of skull analysis to the Tasmanian 
cranium, quite apart from the possession of the skulls or otherwise, and 



1913-14.] Curvatures of the Tasmanian Aboriginal Cranium. 129 

thus Tasmanian cranial work is no longer confined to those fortunate 
centres already mentioned, nor is it impossible now to apply modern 
methods to a race long extinct. It is therefore clear, in view of those 
enormous advantages, that Berry and Bobertson are correct when they say 
“ that all known existing Tasmanian crania, whether in Europe, America, 
or Australia, ought to be similarly recorded, and thus made available for 
study in all parts of the world, and for all time.” 

It will only be by the publication of similar works that any appreciable 
advance will be made in comparative craniological research. So many and 
varied methods of examination have been made on the Tasmanian and 
other crania, that it becomes imperative to secure some suitable method 
by which all the recorded observations may be referred to one common 
standard. 

It is, therefore, most important that similar works on the European 
and other races should be published, so that a detailed system of com- 
parative research may be instituted with the Australian and Tasmanian 
aboriginal crania. 

The morphology and general characters of the Tasmanian crania have 
been the subject of research by such investigators as Barnard Davis (4), 
Topinard (5, 6), de Quatrefages and Hamy (7), Flower (8), Williamson (9), 
Wieger (10), Klaatsch (11), Garson (12), Harper and Clarke (13), Duckworth 
(14), and Turner (15). Still more recently, Berry, Robertson, and Cross (16, 
17, 18) have made some important contributions to the subject, and have 
paid considerable attention to the biometric study of certain cranial obser- 
vations based on Schwalbe’s “ form analysis.” They selected this system 
of investigation in order “ to determine with some degree of certainty 
the final position of the Tasmanian with reference to the anthropoids, 
Pithecanthropus , Homo primigenius , and Homo sapiens, both extinct and 
recent.” They have succeeded, in some measure, in establishing the relative 
position of the Tasmanian aboriginal with the forms just quoted, by 
employing this investigational method. In view of these objects, it was 
absolutely necessary for Berry and Robertson to employ the glabella-inion 
plane as their working base-line, though they agree with Turner that this 
glabella-inion plane is not the best “ from which to estimate the length of 
the cerebral part of the cranial cavity,” for, in their opinion, the nasion- 
inion plane coincides more closely with the cerebral length than either the 
glabella-inion or Turner’s nasio-tentorial plane. 

As the nasion-inion is, therefore, important as a base-line, and as there 
is no reason why the present investigation should not employ it, I have 

directed some attention to it, as also to certain cranial proportions and 
VOL. xxxiv. 9 



130 Proceedings of the Royal Society of Edinburgh. [Sess. 

indices based on it, and referred to later. Two of these curvature indices, 
calculated in accordance with the procedure laid down by Schwalbe (19), 
have already been published by Berry and Robertson. They were 
estimated by taking the proportion which the length of the chord bears 
to the length of the arc, the latter being taken as 100. Klaatsch (20), 
on the other hand, in his work on the Australian and other skulls, 
estimates these indices of curvature quite differently, and says : “ To 
properly appreciate a sloping forehead, the only part of practical im- 
portance is that between the glabella and bregma. The simplest way of 
determining it, though not employed so far as I am aware, is to measure 
the greatest distance of the curved surface of the frontal from the 
glabella-bregma line (i.e. the chord of frontal curvature), and to form 
an index comparing this greatest distance with the length of the glabella - 
bregma line.” 

By multiplying the length of the greatest distance of the chord from 
the arc by 100, aUd dividing by the length of the chord, he constructs his 
index of curvature for the ossa frontale, parietale, et occipitale. It will 
thus be seen that Klaatsch’s index expresses the ratio of the maximum 
distance of arc from chord to the length of the chord, the latter being 
taken as 100. 

I am not at all convinced that the above method will do all that 
Klaatsch endeavours to claim for it. It will, of course, be admitted that 
as a method of determining the amount of curvature it fulfils its purpose ; 
but, in my opinion, it fails to express the degree of the recession of the 
forehead, for, as demonstrated by Schwalbe and others, the sloping forehead 
can only be estimated by angular measurements on a suitable base-line. 
It is, therefore, extremely difficult to see how Klaatsch’s method of dealing 
with the chord of the os frontale and its distance from the arc without the 
use of any base-line whatsoever can express the recession or otherwise 
of the forehead. 

This apart, it is an excellent method of determining the degree of 
curvature of the bone, and is probably preferable to Schwalbe’s method, 
though, it may be noted, the degree of curvature of any cranial bone can 
now be estimated directly by means of Mollison’s cyclometer. 

Turner (21) and Cunningham (22) have also estimated the curvatures of 
various longitudinal osseous segments of the skull in a somewhat similar 
manner to Klaatsch, but do not construct an index of curvature. They 
simply record the greatest distance of the arc from its chord, and, in the 
case of the os frontale, prefer the nasion-bregma or total frontal arc and 
chord to the glabella-bregma measurements. 



TABLE I.— THE INDIVIDUAL AND GENERALISED RESULTS OF 



EXAMINATION OF FIFTY-TWO TASMANIAN ABORIGINAL CRANIA. 



[To face V . 131 . 




Proc. Roy. Soc. Edin ., Yol. XXXIV.] 


Biichner — > 


Probable Sex > 






Serial Number > 


1 


2 


3 






Present Location of Specimen-^ 


Tasmaniai 


Nature of Observation. 


Original Number of Specimen-^ 


4288 


4291 


4300 


“1 


1 


Nasion-Inion Length. 


177 


182 


178 


i 

i 


2 


Bregma Angle. 


59 


60 


+ 

64 


— 


3 


Frontal Angle. 


84*5 


90 


87 


"n 


4 


Lambda Angle. 


78 


80-5 


82 




5 


Opisthion Angle. 


35 


31-5 






6 


Frontal Arc. 


123 


133 


+ 

143 


1 


7 


Frontal Chord. 


108 


114 


116-5 


1 


8 


Greatest Distance of Arc from Chord. 


25 


27 


29 


1 


9 


Occipital Arc. 


122 


119 


110 


1 


10 


Occipital Angle. 


113 


112 




— 

li 


11 


Inion- Opisthion Chord. 


56 


55 




1 

>. 


12 


Total Sagittal Curvature. 


366 


387 


398 


J 


13 


Total Longitudinal Circumference. 


497 


522 




— n 

4 


14 


Vertical Transverse Arc. 


280 


297 


309 


4 


15 


Basal Transverse Diameter. 


143 


+ 

145 


137 


■ 


16 


Total Vertical Transverse Diameter. 


423 


442 


446 


J 


17 


Preauricular Curve. 


226 


239 


260 


% 


18 


Postauricular Curve. 


286 


+ 

294 


279 


A 


19 


Total Horizontal Circumference. 


512 


533 


539 


5 


L. W. G. Buchner. 



1913-14.] Curvatures of the Tasmanian Aboriginal Cranium. 131 

The objects of the present research are : — 

1. To record certain craniometrical curvilinear and angular measure- 
ments, the latter being based on the nasio-inion plane. 

2. To estimate the degree of flattening, or otherwise, of the Tasmanian 
aboriginal crania. 

3. To estimate the evolutionary position of the Tasmanian from a 
study of certain of his cranial curvatures. 

It has already been pointed out that, as one of the main objects of 
the Tasmanian work of Berry and Robertson was a comparison of the 
Tasmanian evolutionary relationship with that of Pithecanthropus erectus , 
they were compelled to employ the glabella-inion plane as their base. As 
the present work is freed from this disability, one of its first objects is to 
restate certain already recorded Tasmanian measurements on the new 
base — the nasio-inion plane — a base which it has already been shown 
Berry and Robertson prefer, where possible. As it is not proposed to do 
more than record these figures, they are simply set forth in Table I , and 
will not herein be again referred to. Suffice it to state that there are now 
available on both base-lines a large number of Tasmanian measurements for 
future comparison of other races by subsequent observers, and that, in each 
instance, the number of Tasmanians so recorded is the largest on record. 

The material on which the present work is based will be found in Berry 
and Robertson’s “ Dioptrographic Tracings in Four Normse of Fifty-two 
Tasmanian Crania ” (23). In Table I. the angular and certain curvilinear 
measurements are estimated from the median sagittal drawings, that is, 
a tracing in the norma lateralis. The remainder of the observations in 
Table I. were recorded by Professor Berry and Dr Robertson on the 
original crania, w r hilst they were engaged in their investigations in 
Tasmania in 1909, and they are now made available for scientific study 
for the first time. I have to express my thanks to these authors for 
permission to utilise their figures. 

These observations, to the number of nineteen, are set forth in 
Table I., and are as follow : — 

1. The nasion-inion length. 

2. The bregma -nasion-inion angle. This angle corresponds with 
Schwalbe’s bregma angle, which has already been recorded by Berry 
and Robertson on the Tasmanian crania which form the subject of the 
present research. 

3. The frontal angle. 

4. The nasion-inion -lambda angle. The lambda angle has already been 
recorded by Berry and Robertson, based on the glabella-inion plane. 



132 



Proceedings of the Royal Society of Edinburgh. [Sess. 



5. The nasion -inion -opisthion angle. Also recorded by Berry and 
Robertson, as the opisthion angle, based on the glabella-inion plane. 

6. The total frontal arc. Nasion to bregma. 

7. The total frontal chord. Nasion to bregma. 

8. The length of the greatest distance of the arc from the chord. 

9. The length of the total occipital arc. Lambda to opisthion. 

10. The occipital angle, enclosed by the lambda-inion and the inion- 
opisthion chords. 

11. The length of the inion-opisthion chord. 

12. The total sagittal curvature. 

13. The total longitudinal circumference. 

14. The length of the vertical transverse arc. 

15. The length of the basal transverse diameter. 

16. The length of the total vertical transverse diameter. 

17. The length of the preauricular curve. 

18. The length of the postauricular curve. 

19. The length of the total horizontal circumference. 

In Table I. the individual and generalised observations just referred to 
of fifty-two Tasmanian crania have been set forth. The probable sex, 
the serial number, the present location, and the original number of each 
skull are set forth in the four upper horizontal lines. In the two vertical 
columns on the left, the numbers and names of the observations recorded, 
and the nature of the observation, are set forth. In the vertical columns 
1 to 52, inclusive, are set forth the individual measurements of each skull. 

The male and female cranial observations have been recorded in separate 
columns. The four vertical columns immediately on the right of the male 
observations record the number of observations made, the average figures 
for each observation together with the minimum and maximum figures 
for that observation. The four vertical columns immediately on the right 
of the female observations record like results, and for both sexes combined 
the figures are set forth in the four vertical columns on the extreme right 
of the Table. 

No. 48 has been shown to be a juvenile subject; all the observations 
recorded upon it have been uniformly omitted from the final results. 

For the purposes of determining the range of variation of each observa- 
tion, the minimum and maximum figures are denoted by means of a 
— or + sign. 

Of the observations set forth in Table I., 4 and 5 and 8 to 12 are 
original ; Nos. 13-19 are the original observations already referred to ; 
Nos. 3, 6, and 7 have already been published by Berry and Robertson 



1913-14.] Curvatures of the Tasmanian Aboriginal Cranium. 133 

(18), but they have been incorporated in the present work for necessary 
reasons. For further explanation of the observations of the median 
sagittal curvatures in Table I., the reader is referred to fig. 1, where the 
method of determining the various measurements is displayed. 

As regards the degree of flattening or otherwise of the Tasmanian 
aboriginal crania, it is very important to notice that Duckworth (24), in 
his recently published (1912) Prehistoric Man, says, “The flatness of a 
cranial arc is but one of many characters awaiting research,” and adds, 



Br 




“ More research is needed.” In the same work, he also states that “ Dr 
Sera (25) has been led to pay particular attention to the remarkably 
flattened cranial vaulting ” of certain crania previously mentioned in 
Duckworth’s work. He also adds that, “as a rule, this flattening has been 
regarded as representative of a stage in the evolution of a highly developed 
type of human skull from a more lowly, in fact a Simian one. This 
conclusion is challenged by Dr Sera. The position adopted is that a 
flattened skull need not in every case owe its presence to such a condition 
as an early stage of evolution assigns to it. Environment, for which we 
may here read climatic conditions, is a possible and alternative influence. 
If sufficient evidence can be adduced to show that the flattened cranial 



134 Proceedings of the Royal Society of Edinburgh. [Sess. 

arc in the Neanderthal skull does actually owe its origin to physiological 
factors through which environment acts, the status of that type of skull 
in the evolutionary sequence will be materially affected. . . . The 
Gibraltar skull is flattened owing to its low place in evolution. But as 
regards the flatness of the brain case (called the platycephalic character) 
of the Neanderthal calvaria and its congeners (as contrasted with the 
Gibraltar specimen) Dr Sera suggests dependence upon the particular 
environment created by glacial conditions.” 

It is thus obvious that the degree of flattening or otherwise is, in view 
of modern opinion, an important present-day field of research, and its 
estimation for the Tasmanian is the chief object of the present work. The 
investigation of the problem is, however, very considerably handicapped 
by the fact that Sera’s original paper is not available in Melbourne, in 
either its original form or in any adequate abstract. With this important 
reservation, I have estimated the degree of curvature, or flattening of the 
glabello-bregmatic arc of the frontal, total parietal arc, and superior 
occipital arc of the os occipitale by Klaatsch’s “index of curvature,” all 
the observations having been made upon the median sagittal plane of the 
Tasmanian life-size tracings already referred to. For a diagrammatic 
explanation of the observations thus recorded, the reader is referred 
to fig. 1. 

The following twelve observations have thus been recorded : — 

Os Frontale. 

1. The length of the glabella-bregma arc. 

2. The length of the glabella-bregma chord. 

3. The length of the greatest distance of the arc from the chord. 

4. The index of frontal curvature (Klaatsch). 

Os Parietale. 

5. The length of the bregma-lambda or parietal arc. 

6. The length of the bregma-lambda or parietal chord. 

7. The length of the greatest distance of the arc from the chord. 

8. The index of parietal curvature (Klaatsch). 

Os Occipitale. 

9. The length of the lambda-inion or superior occipital arc. 

10. The length of the lambda-inion or superior occipital chord. 

11. The length of the greatest distance of the arc from the chord. 

12. The index of occipital curvature (Klaatsch). 

The individual measurements of each of the above, together with 
minimum, average, and maximum results for the whole series of fifty-two 
Tasmanian crania, are set forth in Table II., which is uniform throughout 






f 






TABLE in.— THE INDIVIDUAL AND GENERALISED RESULTS OF THE EXAMINATION OF FIFTY-ONE AUSTRALIAN ABORIGINAL CRANIA. 




Proc. Roy. Soc. Edin Vol. XXXIV.] 



[THE EX AM IN ATI 





Unsexed 




Nature of Observation. 


Serial Number 


23 


24. 


25 


26 


1 


Glabella- Bregma Arc. 


118 


107 


112 


124 


2 


Glabella-Bregma Chord. 


110 


99 


110 


H7[ 


3 


Greatest Distance of Arc from Chord. 


20 


21 


15 


21 


4 


Index of Frontal Curvature (Klaatsch). 


18-1 


21*2 


13*6 


rJ 


5 


Bregma-Lambda Arc. 


120 


117 


120 


131 


6 


Bregma- Lambda Chord. 


110 


107 


114 


123 


7 


Greatest Distance of Arc from Chord. 


23 


23 


22 


24 


8 


1 Index of Parietal Curvature (Klaatsch). 


20-9 


21*4 


19*2 


11 


9 


Lambda- Inion Arc. 


56 


50 


60 


5^ 


10 


Lambda- Inion Chord. 


52 


48 


58 


5; 


11 


Greatest Distance of Arc from Chord. 


9 


6 


8 


4 


12 


Index of Occipital Curvature (Klaatsch). 


+ 

17-3 


12*5 


13*7 


1 



L. W. G. Buchner. 



Proc. Roy. Roc., Min., Vol. XXXIV.] 1 


TY-Tl 


Buchner > 


r 





Nature of Observation. 


Serial Number > 


1 


2 


3 


No. 


1 

2 

3 

4 


The Glabella- Bregma Arc. 


109 


121 


+ 

12{j 


32 

_ 


The Glabella-Bregma Chord. 


103 


111 


+ 

11$ 


32 


The greatest Distance of Arc from Chord. 


19 


20 


j 


32 


The Index of Frontal Curvature (Klaatsch). 


18-4 


18-1 


17f 


32 


5 


The Bregma-Lambda Arc. 


121 


135 


+ 

145 


29 


6 


The Bregma-Lambda Chord. 


111-5 


121 


+ 

127 


30 


7 


The greatest Distance of Arc from Chord. 


23 


26 


+ 

28j 


30 


8 


The Index of Parietal Curvature (Klaatsch). 


19-9 


21-5 


22 


30 


9 


The Lambda- Inion Arc. 


64 


63 


57 


30 


10 


The Lambda- Inion Chord. 


62 


62 


56 


30 


11 


The greatest Distance of Arc from Chord. 


8 


7 


3 


30 


12 ! 


The Index of Occipital Curvature (Klaatsch). 


12-9 


11-1 


5-1 


30 


L. W. G. Buchner. 





1913-14.] Curvatures of the Tasmanian Aboriginal Cranium. 135 



with Table I. As in Table I., No. 48 of Berry and Robertsons Atlas 
is omitted from the final results, as it is known to be a juvenile. 

For comparative purposes I have recorded the same twelve observations 
on forty Australian aboriginal crania. The resulting figures are set forth 
in Table III., in precisely the same manner as those for the Tasmanian in 
Table II. 

In the Australian table I have also included eleven crania from Klaatsch’s 
work, and the entire table thus deals with fifty-one Australian crania, i.e. 
with precisely the same number as there are Tasmanians. 

The source of my own forty original Australian crania is Berry and 
Robertson s“ Dioptrographic Tracings in three Normse of Ninety Australian 
Crania ” (26), now in the press. As only forty of the original drawings 
have as yet been returned from the printer, it was not possible for me to 
utilise the whole ninety. For permission to avail myself of this work 
I have to thank Professor Berry and Dr Robertson. My Australian 
material will eventually be found, therefore, to include plates numbered 
1 to 40, norma A, of the atlas of tracings just referred to. The whole of 
this series of Australian crania is quite new, and has not previously been 
recorded scientifically. 

The indices of curvature of the several segments of the median sagittal 
curve of the fifty-one Tasmanian and fifty-one Australian crania may be 
summarised and compared with certain selected objects recorded by Klaatsch, 
as follow : — 

Curvature index of glabello-bregmatic curve of the os frontale : — 



1 Pithecanthropus erectus (Klaatsch) 
3 Spy-Neanderthal (Klaatsch) . 

51 Australians (Klaatsch and Buchner) 
51 Tasmanians (Buchner) . 



7*53 

133 

181 

18*7 



As Klaatsch’s index of curvature expresses the ratio which the length 
of the greatest distance of the arc from the chord bears to the length of 
the chord, the latter being taken as 100, it follows from the above that the 
Tasmanian possesses the most highly curved glabello-bregmatic arc of any 
of the objects compared. 

The curvature index of the os parietale, as worked out by Klaatsch’s 
method, and compared with the same objects as before, is as follows : — 



1 Pithecanthropus erectus (Klaatsch) . . . 9*68 

3 Spy-Neanderthal (Klaatsch) ..... 17*04 

51 Australians (Klaatsch and Buchner) . . . 20*2 

51 Tasmanians (Buchner) ...... 20*5 



136 



Proceedings of the Royal Society of Edinburgh. [Sess. 



Here again the Tasmanian possesses the most highly curved parietal 
arc, whilst the Australian again occupies third place, a little inferior to the 
Tasmanian. If these results be read in association with the known 
physiological functions of those portions of the brain which lie subjacent 
to the parietal arc, they become of real and striking significance. 

Dealing in the same way with the superior occipital index of curvature, 
we achieve the following results : — 



1 Pithecanthropus erectus (Klaatsch) 
51 Australians (Klaatsch and Buchner) 
51 Tasmanians (Buchner) . 

3 Spy-Neanderthal (Klaatsch) . 



. 4*76 

. 10-9 

. 11 T 

. 14T7 



Here the several objects have changed places — the Spy-Neanderthal group 
having the most highly curved superior occipital arcs, whilst the Tasmanian 
still retains his more advanced position over the Australian. It is difficult 
to account for the increased degree of superior occipital curvature in the 
Spy-Neanderthal group, but as regards the Australians and Tasmanians 
it is interesting to observe that, in all its segments, the median sagittal 
curvature of the Australian calvaria is less pronounced than in the 
Tasmanian, that is, the Australian has a flatter skull, as regards curvature, 
than has the Tasmanian. 

In a previous publication (27) I recorded the range of variation 
on fifty-two Tasmanian crania for twenty-seven observations based on 
Klaatsch’s cranio-trigonometrical methods. The figures expressive of this 
range of variation were so small as to warrant the conclusion which I then 
drew, that the Tasmanian is a pure race. By totally different methods 
Berry and Robertson (28), in a memoir as yet unpublished, but now ready 
for the press, have arrived at identical conclusions. 

I have, therefore, again recorded the range of variation for the twelve 
observations set forth in Table II. of the present work, in order to ascertain 
if my former conclusions would be sustained. 

The results attained from the present and previous works just referred 
to are, for the Tasmanian, as follows : — 



Present Work. 

Degree of Sagittal Curvature. 

Males .... 8*9 

Females . . 7 ’8 

Both sexes . . . 10 3 



Previous Work. 

Twenty-seven Cranio-trigonometrical 
Observations. 

Males . . . .7-9 

Females . . .7*5 

Both sexes . . . 9’9 



1913-14.] Curvatures of the Tasmanian Aboriginal Cranium. 137 

The range of variation of the combined observations, from these two works, 
is therefore, for the Tasmanian, as follows :• — 

Males 8*4 

Females ..... 7*6 

Both sexes . . . .10*1 

The manner of estimating the range of variation by a single figure was 
dealt with in my previous work. The result is so surprisingly low 
as to justify the statement already made, that the Tasmanian is a homo- 
geneous race. 

Passing now to the third and last purpose of the present work, namely, 
an estimate of the evolutionary position of the Tasmanian, as deduced from 
a study of the relative degree of curvature of the various segments of the 
calvaria as herein described, I propose to deal with the subject on somewhat 
similar lines to those adopted by Berry and Robertson. 

It will be remembered that these authors, in conjunction with Dr Cross, 
introduced some strikingly original methods, in their attempt to place the 
Tasmanian in his correct evolutionary position as compared with certain 
supposed lower morphological forms. Their work was based solely on 
twenty-seven of the “ form analysis ” measurements of Schwalbe, and it 
seems to me desirable to ascertain if their final conclusions will be 
sustained by like methods based on completely different observations. 

With this object in view, I shall, therefore, deal with the degree of 
flattening of the skull as studied in this work, and I shall employ as 
objects of comparison the crania of the chimpanzee, Pithecanthropus 
erectus, Gibraltar, Spy-Neanderthal, Brtix, Galley Hill, Brunn, Cro-Magnon, 
Australian, Tasmanian, and European. 

The sources from which I have obtained the necessary data are as 
follow : — 

For the anthropoid I have utilised certain observations already 
published by Berry and Robertson (18). 

For Pithecanthropus I have utilised the necessary observations already 
recorded by Klaatsch (20) in his memoir on the Australian skull. 

For the Gibraltar skull the observations have been calculated from the 
diagrams furnished by Sollas (29). 

For the Spy-Neanderthal group the observations have been calculated 
from median sagittal diagrams in Schwalbe’s monograph on Pithecan- 
thropus erectus (19). 

For the Briix, Galley Hill, Briinn, and Cro-Magnon crania the observa- 
tions have been calculated by me from median sagittal diagrams furnished 
by Schwalbe (30) and Klaatsch (31). 



138 Proceedings of the Royal Society of Edinburgh. [Sess. 

The Australian and Tasmanian measurements are the original con- 
tributions to the subject of the present work. 

For the European the observations have already been recorded by 
Klaatsch. 

In grouping these several objects of comparison together for purposes 
of calculation, I have regarded the Neanderthal and Spy crania as a 
homogeneous group, and have dealt with the Galley Hill, Brux, and Brtinn 
crania in a like way, and for like reasons. To the former procedure there 

Cro-Magnon. 

European. 

Galley Hiil-Brux-Briinn. 

Tasmanian. 

Australian. 

Spy-Neanderthal. 



Gibraltar. 



Pithecanthropus erectus. 

Anthropoid ape. 

Fig. 2. 

can be no objection, and for the inclusion of the Galley Hill skull with 
those of Brux and Briinn I have been largely influenced by the recently 
expressed opinions of Duckworth (24). 

For the mathematical estimation of the relative evolutionary positions 
of the Tasmanian and the other objects of comparison, I have adopted the 
ingenious methods introduced by Cross. I have not, however, deemed it 
necessary to prolong the calculations beyond what Cross terms the 
“ composite order.” The working of the method is illustrated in Tables 
IV., V., and VI. 



1913-14.] Curvatures of the Tasmanian Aboriginal Cranium. 139 

The final result is displayed graphically in fig. 2, and numerically in 
Table VI. 

Table IV. 



Nature of Observation. 


Anthropoid. 


Pithecanthropus. 

1 


Spy- Neanderthal. 


Gibraltar. 


Galley Hill- 
Brux-Biiinn. 


Australian. 


d 

‘3 

3 

0Q 

as 

EH 


Cro-Magnon. 


European. 


1 


Glabella-Bregma Arc . 


92 


no 


124 




135 


110-2 


119-9 


138 




2 


Glabella-Bregma Chord 


87 


93 


108 




119 


108 


105-2 


123 


no’ 


3 


Greatest Distance of 
Arc from Chord 




7 


14-3 




| 20-7 


19-6 


18-8 


24 


24 


4 


Index of Frontal Cur- 
vature 




753 


13T3 




17-5 


18-1 


18-7 


19-5 


21-8 


5 


Bregma-Lambda Arc . 


62 


103 


119-6 




126-6 


121-2 


125-8 


135 


133 


6 


Bregma-Lambda Chord 




93 


112 


... 


116-3 


114-7 


113 


123 


112 


7 


Greatest Distance of 
Arc from Chord 




9 


18-3 




21 


23-2 


23 3 


26-5 


24 


8 


Index of Parietal Cur- 
vature 




9-68 


17-04 




17-3 


20-2 


20-5 


21-6 


21-4 


9 


Lambda-Inion Arc 




30 


57*3 


58-5 


60 


55-7 


58-5 


63 




i 10 


Lambda-Inion Chord . 




42 


54 


38 


60-6 


55-2 


55-5 


60-75 


63 


11 


Greatest Distance of 
Arc from Chord 




2 


7-6 


5 


8-2 


6-1 


6-1 


8 2 


11 


12 


Index of Occipital Cur- 
vature 




4-76 


14-17 


13*1 


13-3 


10-9 


11-1 


13*4 


17-46 



Table V. 





Nature of Observation. 


Maximum. 


| Anthropoid. 


Pithecanthropus. 


Spy-Neanderthal. 


Gibraltar. 


Galley Hill- 
Briix-Briinn. 


Australian. 


Tasmanian. 


1 Cro-Magnon. 


European. 


1 


Glabella-Bregma Arc . 


46 


0 


18' 


32 




43 


18-2 


19-9 


46 




2 


Glabella- Bregma Chord 


36 


0 


6 


21 




32 


21 


18-2 


36 


23 


3 


Greatest Distance of Arc 
from Chord 


17 




0 


7-3 




13-7 


12-6 


11-8 


17 


17 


4 


Index of Frontal Curvature 


14-3 




0 


5-6 




10 


10-6 


11-2 


12 


14-3 


5 


Bregma-Lambda Arc . 


73 


o' 


41 


57-6 




64-6 


59-2 


63-8 


73 


71 


6 


Bregma-Lambda Chord 


30 




0 


19 




23-3 


21-7 


20 


30 


19 


7 


Greatest Distance of Arc 
from Chord 


17-5 




0 


9-3 




12 


14-2 


14-3 


17-5 


15 


8 


Index of Parietal Curvature 


11-92 




0 


7-36 




7-62 


10-52 


10-82 


11-92 


11-72 


9 


Lambda-Inion Arc 


33 


| 


0 


27-3 


28-5 


30 


25-7 


28-5 1 


33 




10 


Lambda-Inion Chord . 


25 | 




4 


16 


0 


22-6 


17-2 


17-5 


22-8 


25 


11 


Greatest Distance of Arc 
from Chord 


9 




0 


5-6 


3 


6-2 


41 


4T 


6-2 


9 


| 12 

1 


Index of Occipital Curvature 


12-7 




0 


9-41 


8-34 


8'54 


6T4 


6-34 


8-54 


12-7 



140 Proceedings of the Royal Society of Edinburgh. [Sess. 

Concerning the Tasmanian and Australian, it will be seen that these 
results confirm absolutely the conclusions previously drawn by Berry, 
Robertson, and Cross ; and it will also be subsequently found that, as regards 
the placing of the Australian on the minus side of the Tasmanian, these 
results confirm those about to be published by Berry and Robertson (28). 

The Gibraltar skull appears herein between Pithecanthropus erectus 
and the three Spy-Neanderthal crania. This lowly position may, however, 



Table VI. 





Nature of Observation. 


Number. 


Anthropoid. 


Pithecanthropus. 


Spy- N ean d erthal . 

____ 


Gibraltar. 


Galley Hill- 
Brux-Briinn. 

i 


Australian. 


o3 

S3 

g 

02 

Eh 


Cro-Magnon. 


European. 


1 


Glabella-Bregma Arc 


6 


0 


2*35 


4-17 


[ 


5-61 


2-37 


2*60 


6-00 




2 


Glabella-Bregma Chord . 


7 


0 


l'I7 


4-08 




6*22 


4-08 1 


3-54 


7*00 


4-47 


3 


Greatest Distance of Arc 
from Chord . 


6 




0 


2-58 




4-84 


4-45 1 


i 4T6 


6-00 


6-00 


4 


Index of Frontal Curva- 
ture .... 


6 




0 


2*35 




4-20 


4-45 


4-70 


5-04 


6*00 


5 


Bregma-Lambda Arc 


7 


0 


3 93 


5*52 




6T9 


5-68 


6T2 


7-00 


6-81 


6 


Bregma-Lambda Chord . 


6 




0 


3-80 




4-66 


4-34 


4*00 


6-00 


3-81 


7 


Greatest Distance of Arc 
from Chord . 


6 




0 


3*19 




4T1 


GO 


4-90 


6-00 


5-14 


8 


Index of Parietal Curva- 
ture .... 


6 




0 


3-70 




3-84 


5-30 


5-45 


6-00 


5*90 


9 


Lambda-Inion Arc . 


6 




0 


4-96 


5T8 


5-45 


4-67 


5T8 


6-00 




10 


Lambda-Inion Chord 


7 




1T2 


4-48 


0 


6 33 


4-82 


4-90 


63-8 


7-00 


11 


Greatest Distance of Arc 
from Chord . 


7 




0 


4-35 


233 


4-82 


3T9 


3T9 


4-82 


7*00 


12 


Index of Occipital Curva- 
ture .... 


7 




0 


5T9 


4-60 


471 


3-38 


3-49 


4-71 


7-00 




Total .... 




0 


8-57 


48-38 


12T1 


60-98 


51-60 


52-23 


70-95 


59T2 




Possible Maximum . 




20 


77 


77 


27 


77 


77 


77 


77 


65 




Relative Position 




0 


•111 


•628 


•315 

1 


•792 


•670 


•678 


•921 


•912 



be due to the fact that I have only dealt with four measurements, inasmuch 
as it is well known that the Gibraltar calvaria is imperfect; or, on the 
other hand, it may be really due to the lowly position claimed for 
this skull by Keith and others. 

That the Galley Hill-Brux-Briinn group appear on the plus side 
of the Tasmanian-Australian series need cause no surprise, because they are 
herein dealt with as a group, and not singly as in Cross’s work. Even the 
latter observer placed one of them on the plus side and the other two on 
the immediate minus side of the Tasmanian. 



1913-14.] Curvatures of the Tasmanian Aboriginal Cranium. 141 

Working, then, on totally different craniological lines, it is sufficiently 
obvious that, as regards the Tasmanian-Australian type — the “ Hesper- 
anthropus tasmanianus, spec.” of Sergi, — the present work sustains the 
thesis of Berry and Robertson that the “ lately extinct Tasmanians recall 
the mental level of eolithic man in Britain we can quite believe ; but that 
either the Australian or the Tasmanian carries us back nearly to the 
Neanderthal physical type, we must, as the result of the present investiga- 




tion, deny, because the physical construction of the Tasmanian is herein 
certainly shown to go back only so far as the Galley Hill type at furthest, 
and more than this cannot be maintained with any degree of scientific 
certainty.” 



REFERENCES. 

(1) Berry, R. J. A., and A. W. D. Robertson, “Preliminary Communication 
on 'Fifty-three Tasmanian Crania, forty-two of which are now recorded for the 
first time,” Proc. Roij. Soc. of Viet., vol. xxii., N.S., pt. i., 1909, pp. 47-58. 

(2) Berry, R. J. A., and A. W. D. Robertson, “Preliminary Account of the 
Discovery of Forty-two hitherto unrecorded Tasmanian Crania,” Anat. Anz., Bd. 
xxxv. pp. 11-17, 1909. 



142 



Proceedings of the Royal Society of Edinburgh. [Sess. 

(3) Sergi, G., “ Tasmanier und Australier, Hesperanthropus tasmanianus , 
spec.,” Arclniv fur Anthrop ., Neue Folge, Bd. xiii., Heft 3, 1912. 

(4) Barnard Davis, “ Osteology and Peculiarities of the Tasmanians,” Natuur. 
Kund. Verhandl. der Hollandsche Maatschap. der Wetenschap, 3 verz., Deel ii., 
No. 4, Haarlem, 1874. 

(5) Topinard, P., “ Etude sur les Tasmaniens,” Mem. de la Soc. d’ Anthropologie, 
tome iii. p. 307, 1872. 

(6) Topinard, P., “ Examen des mesures craniometriques adoptees par le 
Thesaurus Craniorum de Barnard Davis et en particulier de celles de la serie des 
Tasmaniens,” Revue d’ Anthropologies tome ii. p. 99, 1873. 

(7) Quatrefages and Hamy, Crania Ethnica , Texte et Atlas, Paris, 1882. 

(8) Flower, W. H., Osteological Catalogue , Museum Royal College of Surgeons 
of England, pt. i., “Man,” London, 2nd edition, 1907. 

(9) Williamson, G., “ Observations of the Human Crania in the Museum of 
the Army Medical Department, Fort Pitt, Chatham,” Dub. Journ. Med. Science , 
vol. xxiii., vol. xxiv. p. 42, May and August 1857. 

(10) Wieger, G., Katalog der anthropologischen Sammlung des Anatom ischen 
Institute zu Breslau, Festgabe, Braunschweig, 1884. 

(11) Klaatsch, H., “Bericht ueber einen anthrop. Streifzug nach London,” 
Zeit.f. Eihnologie, Heft 6, p. 875, 1903. 

(12) Garson, J. G., Chapter on “Osteology” in Ling Roth’s The Aborigines of 
Tasmania, 1899. 

(13) Harper, W. E., and A. H. Clarke, “Notes on the Measurements of the 
Tasmanian Crania in the Tasmanian Museum, Hobart,” Papers and Proc. Roy. Soc. 
Tasmania , 1897, pp. 97-110. 

(14) Duckworth, W. L. H., “ Craniological Notes on the Aborigines of 
Tasmania,” Journ. Anthrop. Inst., vol. xxxii. p. 177, 1902; and Studies from the 
Anthropological Laboratory, Cambridge, 1904. 

(15) Turner, Sir W., “The Aborigines of Tasmania: pt. ii., The Skeleton,” 
Trans. Roy. Soc. Edin., vol. xlvii., pt. iii. (No. 16), pp. 411-454, 1910. 

(16) Berry, R. J. A., A. W. D. Robertson, and K. S. Cross, “A Biometrical 
Study of the Relative Degree of Purity of Race of the Tasmanian, Australian, and 
Papuan,” Proc. Roy. Soc. Edin., vol. xxxi., pt. i. (No. 2), 1910. 

(17) Cross, K. S., “On a Numerical Determination of the Relative Positions of 
certain Biological Types in the Evolutionary Scale, and of the Relative Values 
of various Cranial Measurements and Indices as Criteria,” Proc. Roy. Soc. Edin., 
vol. xxxi., pt. i. (No. 4), 1910. 

(18) Berry, R. J. A., and A. W. D. Robertson, “ The Place in Nature of the 
Tasmanian Aboriginal as deduced from a Study of his Calvaria : pt. i., His 
Relations to the Anthropoid Apes, Pithecanthropus , Homo primigenius , Homo 
fossilis , and Homo sapiens ,” Proc. Roy. Soc. Edin., vol. xxxi., pt. i. (No. 3), 1910. 

(19) Schwalbe, G., “Studien iiber Pithecanthropus erectus Dubois,” Zeitschrift 
fur Morphologie und Anthropologie, Bd. i., Heft 1, p. 16 et seq., 1899. 

(20) Klaatsch, H., “The Skull of the Australian Aboriginal,” Reports from the 
Path. Lab. of the Lunacy Dept. N.S. W., vol. i. p. 45 et seq. 



1913-14.] Curvatures of the Tasmanian Aboriginal Cranium. 143 

(21) Turner, Sir W., “The Craniology, Racial Affinities, and Descent of the 
Aborigines of Tasmania,” Trans. Roy. Soc. Edin., vol. xlv., pt. ii. (No. 17), 
pp. 365-403, 1908. 

(22) Cunningham, D. J., “The Australian Forehead,” Anthropological Essays 
presented to E. B. Tylor, 1907. 

(23) Berry, R. J. A., and A. W. D. Robertson, “ Dioptrographic Tracings in 
Four Normse of Fifty-two Tasmanian Crania,” Trans. Roy. Soc. Viet., vol. v., 1910. 

(24) Duckworth, W. L. H., Prehistoric Man , Cambridge, 1912. 

(25) Sera, Dr, Archivio jper V Antropologia e per la Etnologia , xl., fasc. 3-4, 
quoted by Duckworth under (24). 

(26) Berry, R. J. A., and A. W. D. Robertson, “ Dioptrographic Tracings in 
Three Normse of Ninety Australian Crania,” now in the press, Trans. Roy. Soc. 
Viet. 

(27) Buchner, L. W. G., “An Investigation of Fifty-two Tasmanian Crania by 
Klaatsch’s Cranio-trigonometrical Methods,” Proc. Roy. Soc. Viet., vol. xxv., new 
series, pt. i., pp. 122-135, 1912. 

(28) Berry, R. J. A., and A. W. D. Robertson, “The Place in Nature of the 
Tasmanian Aboriginal, as deduced from a Study of his Calvaria : pt. ii., His Relation 
to the Australian Aboriginal,” Proc. Roy. Soc. Edin., vol. xxxiv., pt. ii.. No. 12, 1914. 

(29) Sollas, W. J., “ On the Cranial and Facial Characters of the Neanderthal 
Race,” Phil. Trans., B, vol. exeix., 1907. 

(30) Schwalbe, G., “Das Schadelfragment von Briix und verwandte Schadel- 
formen,” Zeit.fiir Morph, und Anthrop., Sonderheft, Mai 1906. 

(31) Klaatsch, H., “ Die Fortschritte der Lehre von den fossilen Knochen- 
resten des Menschen in den Jahren 1900-1903,” Merkel und Bonnet's Ergebnisse 
der Anatomie und Entioickelungsgeschichte, vol. xii. pp. 545-551, 1903. 



{Issued separately April 28, 1914.) 



144 



Proceedings of the Royal Society of Edinburgh. [Sess. 



XII. — The Place in Nature of the Tasmanian Aboriginal as 
deduced from a Study of his Calvaria. — Part II. His Rela- 
tion to the Australian Aboriginal. By Richard J. A. Berry, 

M.D. Edin., Professor of Anatomy in the University of Melbourne; 
and A. W. D. Robertson, M.D. Melb., Government Research 
Scholar in the Anatomy Department of the University of 
Melbourne. (With One Folding Table.) 

(MS. received December 9, 1912. Read January 19, 1914.) 

Introduction. 

In December 1910 we published, in conjunction with Dr K. Stuart Cross, 
in the Proceedings of the Royal Society of Edinburgh (1, 2, 3, 4) a series 
of four papers dealing with the relations of the Tasmanian aboriginal to 
Pithecanthropus erectus and to primitive man generally. In an earlier 
publication, published in the Transactions of the Royal Society of Victoria 
(5), we also made available the material upon which our Tasmanian work 
was based. In the present publication we propose to deal with the 
question of the relationship of the Tasmanian aboriginal to the Australian, 
with a view to deciding, if possible, the vexed questions as to whether 
the Tasmanian and the Australian are one and the same race, or, if not, 
if the Australian is a homogeneous or a heterogeneous race. 

Literature. 

In one of our previous communications (2) we have dealt fairly ex- 
haustively with the views of the two opposed schools into which the 
study of the Australian aboriginal has divided scientific ethnologists. 
On the one hand there are Keane, Flower and Lydekker, Topinard, Tylor, 
Curr, de Quatrefages, and Mathew, who hold the Australian to be an 
impure race — that is, to have resulted from a cross; on the other hand 
there are Klaatsch, Schoetensack, and other German savants, who hold 
that the Australian is a pure type and that the Tasmanian is but an 
insular variation of that type. This subject has also been still further 
dealt with by one of us in another publication (6), so that it is unnecessary 
here to pursue the question further. The more recent literature bearing 
on this question will be dealt with as occasion demands in the subsequent 
parts of this paper. 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 145 

Sources of the Material. 

For the purely Australian part of the present investigation we have 
availed ourselves of 100 Australian aboriginal crania, none of which 
have ever previously been examined by any scientist. Of these, numbers 
1 to 50, both inclusive, are from the Anatomy Museum of the University 
of Melbourne : the remaining 50 are from the National Museum, Melbourne ; 
and for their use we have to thank the Director of the Museum, Professor 
Spencer, as also his assistants, Messrs Kershaw and Walcott. 

Of these 100 crania it is most important to note that all with the 
exceptions of numbers 43 to 50, both inclusive, are Victorian crania ; the 
eight exceptions are from Queensland. It follows therefore that 92 per 
cent, of our Australian crania are derived from sources in the vicinity 
of the Murray River, or roughly from a district south of the thirty-fifth 
parallel of latitude ; the importance of this lies in the fact that there 
cannot be any question of racial impurity due to admixture with the 
Malay element, which is not infrequently the case with Australian crania 
derived from the Northern Territory or other portions of the Australian 
Continent in the vicinity of the Malay Peninsula. 

For the purposes of comparison with the Tasmanian, our material is 
naturally that of our recent Tasmanian work, to which reference has 
already been made. 

For other comparative purposes, to which reference will subsequently 
be made, we have availed ourselves of material derived from the Catalogue 
of the Royal College of Surgeons of London. The material so utilised 
comprised 19 Andamanese Islander crania, and 90 crania of modern 
Italians. 

In addition to this we have also availed ourselves of certain data 
published by Schwalbe for the Spy-Neandertal group of crania. 

Technique. 

In the case of the 100 Australian aboriginal crania dioptrographic 
tracings in four normse were recorded of all by means of Martin’s 
dioptrograph, each skull being orientated in the Frankfort plane in the 
Kubuskraniophor. Selections from these tracings are now in the printer’s 
hands, and will be published in due course. 

Observations recorded. 

On the dioptrographic tracings there have been recorded the measure- 
ments of the 27 observational counts previously employed by us in the 

VOL. XXXIV. 10 



146 



Proceedings of the Royal Society of Edinburgh. [Sess. 

Tasmanian work, and to which the reader is referred. These, it will be 
remembered by those who have seen that work, are the data employed 
by Schwalbe in his examination of the Pithecanthropus, Spy, Neandertal, 
and other calvaria. To these 27 observations there have been added, in 
the case of the Australian, 5 other observations employed by Klaatsch 
(7), as follows : — 

A. The nasio-inion length. 

B. The glabella-lambda length. 

C. The lambda-glabella-inion angle. 

D. The distance of the bregma foot-point from the glabella on the 

glabelladambda line. 

E. The bregma foot-point-glabella-lambda index — that is, the proportion 

which the distance of the bregma foot-point from the glabella 
on the glabella-lambda line bears to the glabella-lambda length, 
the latter being taken as 100. 

The complete series of measurements employed will be readily seen 
in fig. 1. 

In addition to the foregoing 32 observational points of the form analysis 
of the Australian aboriginal skull, we have also recorded and employed for 
purposes of comparison a second series of ordinary craniological observa- 
tions as follows : — 

1. Maximum cranial length. 

2. Maximum cranial breadth. 

3. The cephalic index. 

4. Cranial height. 

5. The height index. 

6. The basi-nasal length. 

7. The basi-alveolar length. 

8. The alveolar index. 

9. The nasal height. 

• 10. The nasal width. 

11. The nasal index. 

12. The orbital width. 

13. The orbital height. 

14. The orbital index. 

The necessary figures for the above in the cases of the Australian and 
Tasmanian have been obtained from our own original material. In the 
cases of the Andamanese Islanders and the modern Italians they have been 
obtained from the Catalogue of the Royal College of Surgeons of London. 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 



147 




Fig. 1 . — Median Sagittal Section through an Adult Male Australian Aboriginal Skull. (Victoria 
No. 18 . From the Anatomical Museum of the University of Melbourne.) To illustrate 
Schwalbe’s form analysis of the skull, as employed in the present investigation. 



X. The nasion. 

G. The glabellar point. 

A. The upper limit of the glabellar curve. 

P. The maximum point of the frontal curvature. 

B. The bregma. 

C. The maximum point of the calvarial height. 

X. The maximum point of the parietal curvature. 
L. The lambda. 

I. The in ion. 

0. The opisthion. 

H. The calvarial height foot-point. 

G.I. The glabella-inion length. 

G.L. The glabella-lambda length. 

N.I. The nasio-inion length. 

C.H. The calvarial height. 

D. The bregma foot-point on the glabella-inion 

line. 

E. The bregma foot-point on the glabella-lambda 

line. 



Gr.H. The distance of the calvarial height foot- 
point from the glabella. 

G.I). The distance of the bregma foot-point from 
the glabella on glabella-inion line. 

G.E. The distance of the bregma foot-point from 
the glabella on glabella-lambda line. 

B.G.I. The bregma angle. 

F. G.I. The frontal angle. 

N.B. The frontal chord. 

N.A. The glabellar chord. 

A. B. The cerebral chord. 

B. L. The parietal chord. 

G. P.B. The angle of frontal curvature. 

B.X.L. The angle of parietal curvature. 

L.I.G. The lambda angle. 

L.G.I. The lambda-glabella-inion angle. 

O.I.G. The opisthionic angle. 



148 



Proceedings of the Royal Society of Edinburgh. [Sess. 



The 32 Form Analysis Measurements of the Australian Skull. 

For the display of the 32 observational counts made upon each one of 
the hundred Australian aboriginal crania with which this memoir deals, 
we propose, for purposes of comparison, to adopt the same procedure 
as employed by us in our former work upon the Tasmanian (3). The 
individual results of the entire series of 100 crania are, therefore, set forth 
in a table of measurements (Table XXVIII.). This table will form a 
valuable means of comparison and contrast with the similar table published 
by us for the Tasmanians (3), the more so as the two tables deal with what 
is probably the largest consecutive series of Tasmanian and Australian 
crania yet dealt with, namely, 52 Tasmanian and 100 Australian crania. 

In the Tasmanian work just referred to, in addition to publishing a 
complete table of all measurements, we dealt with each observational count 
separately. This procedure was adopted in order to form a first estimation 
of the evolutionary position occupied by the Tasmanian under each observa- 
tional count. We regard it as important to form a like opinion for the 
Australian, so that it is necessary, even at the risk of reiteration, to record 
the same tables here with the Australian included. We have, however, taken 
the opportunity whenever it was afforded, to increase the numbers of the 
objects of comparison. In the several tables now to follow the results are 
set forth, just as they were for the Tasmanian, in a progressive series from 
the lowest figure to the highest, or in the reverse way according to the scale 
of evolution, and each table also shows not only those with which the com- 
parison is made, but also those which are excluded from the comparison. 



Table I. — Comparison of the Calvarial Height (Kalottenhohe). 





Minimum. 


Average. 


Maximum. 


1. An adult male chimpanzee 




48*5 




2. Pithecanthropus erectus .... 




62 




3. Gibraltar ...... 




85 




4. Briix 




85 




5. Three Spy-Neandertal .... 


81 


85-3 


88 


6. Four Kalmucks 


88 


90-7 


94 


7. One hundred Australians, unsexed . 


79-5 


95 


108 


8. Galley Hill ...... 




97 




9. Forty-eight Tasmanians, unsexed 


87 


97 


108 


10. Eight Veddahs 


94 


99-2 


107 


11. Thirty-four Europeans, unsexed 


91 


99-9 


115 


12. Twenty-three Dschagga negroes 


84 


100 


1155 


13. Egisheim 




100 




14. Cro-Magnon ...... 




101 




15. Briinn 




103 




16. Stangenas ...... 




106 





1913-14.] The Place in Nature of the Tasmanian Aboriginal. 149 



Table II. — Angle of Frontal Curvature measured on the Glabella 

Bregma Chord. 





Minimum. 


Average. 


Maximum. 


1. An adult Gibbon 




160 




2. Three Spy-Neandertal .... 


150 


153-3 


159 


3. Pithecanthropus erectus .... 


148-5 


153-2 


158 


4. One hundred Australians, unsexed . 


123-5 


139-6 


153 


5. Fifty Tasmanians, unsexed 


131-5 


139-5 


149 


6. Seven Europeans ..... 


127 


135-4 


148 


7. Four Dschagga negroes .... 


122 


131-5 


136-5 



Gibraltar, Briix, Galley Hill, Brunn, Cro-Magnon, Veddahs, Kalmucks, 
Egisheim, and Stangenas absent. 



Table III. — Comparison of the Calvarial Height -Breadth Index. 





Minimum. 


Average. 


Maximum. 


1. An adult male chimpanzee 




42-9 




2. Pithecanthropus erectus .... 




46-6 




3. Three Spy-Neandertal .... 


55-4 


56-7 


57-9 


4. Gibraltar ...... 




57-4 




5. Four Kalmucks ..... 


62-1 


63-3 


64-8 


6. Briix ....... 




63-3 




7. Cro-Magnon ...... 




66-8 




8. Forty-four Tasmanians, unsexed 


65-9 


72-2 


79-2 


9. Four Europeans, unsexed 


69 


72-4 


76-2 


10. One hundred Australians, unsexed . 


60-2 


72-7 


85-4 


11. Briinn ....... 




74-1 




12. Galley Hill 




74-6 




13. Four Veddahs ..... 


69-6 


76-9 


82-9 



Dschagga negroes, Egisheim, and Stangenas absent. 



Table IV. — Comparison of the Bregma Angle. 



1. An adult male chimpanzee 

2. Pithecanthropus erectus . 

3. Three Spy-Neandertal 

4. Gibraltar .... 

5. Briix 

6. Galley Hill .... 

7. Stangenas .... 

8. Brunn ..... 

9. Cro-Magnon .... 

10. One hundred Australians, unsexed 

11. Forty-five Tasmanians, unsexed 

12. Four Kalmucks 

13. Egisheim .... 

14. Twenty-four Dschagga negroes 

15. Forty Europeans 



Minimum. 


Average. 


Maximum. 




39-5 




34 


37-5 


41* 


45 


47-5 


50-5 


50 


50-5 


51 




51-1 






52 






52-5 






54 






54 




49 


54-7 


60 


51-5 


56 


64 


55 


56-5 


57 




58 




53 


58-6 


63-5 


54 


59-9 


68 



Veddahs absent. 



* Employed for comparative purposes. 



150 Proceedings of the Royal Society of Edinburgh. [Sess. 



Table V. — Comparison of the Calvarial Height Index (Kalottenhohen-Index.) 





Minimum. 


Average. 


Maximum. 


1. Pithecanthropus erectus .... 




34-2 




2. An adult male chimpanzee 




35-1 




3. Three Spy-Neandertal .... 


40-9 


44-9 


47 


4. Gibraltar 




45-4 




5. Briinn 




47*6 




6. Galley Hill ...... 




48-2 




7. Cro-Magnon ...... 




50 




8. Briinn 




51-2 




9. One hundred Australians, unsexed . 


44-9 


53 


61-5 


10. Four Kalmucks ..... 


52*8 


54-5 


84-9 


11. Stangenas 




54*6 




12. Egisheim ...... 




55-5 




13. Forty-four Tasmanians, unsexed 


48-3 


56-1 


62-7 


14. Eight Veddahs ..... 


54-6 


58*4 


62-9 


15. Twenty- three Dschagga negroes 


52-1 


59-8 


67-1 


16. Thirty- two Europeans .... 


54-4 


59-8 


66-2 



Table VI. — Comparison of the Calvarial Height Half-Sum Glabella-Inion 
Length plus Breadth Index. 





Minimum. 


Average. 


Maximum. 


1. An adult male chimpanzee 




38-6 




2. Pithecanthropus erectus .... 




39-4 




3. Three Spy-Neandertal .... 


47 


48-9 


50 


4. Gibraltar 




50-7 




5. Galley Hill 




50-8 




6. Briix 




54*8 




7. Cro-Magnon ...... 




57-2 




8. Four Kalmucks ..... 


57-1 


58-7 


60-2 


9. Briinn 




60-5 




10. One hundred Australians, unsexed . 


52-3 


61-3 


69-9 


11. Forty-four Tasmanians, unsexed 


55-2 


63 


69-5 


12. Five Europeans, unsexed 


60-9 


65-8 


69-8 


j 13. Four Veddahs ..... 


61-2 


66-6 


71-5 



Egisheim, Stangenas, and Dschagga negroes absent. 



Table VII. — Comparison of the Length of the Parietal Arc. 





Minimum. 


Average. 


Maximum. 


1. An adult female chimpanzee . 




62 




2. Pithecanthropus erectus .... 


93 


103 


113 


3. Briix 




108 




4. Gibraltar ...... 




111 




5 Seventeen Maories, unsexed 


101 


117 


127 


6. Three Spy-Neandertal .... 


119 


119-6 


120 


7. Forty-eight Tasmanians, unsexed . 


112 


125-8 


145 


8. One hundred Australians, unsexed . 


109 


125-9 


147 


9. Galley Hill 




132 




10. One European ..... 




133 




11. Cro-Magnon ...... 




135 




12. Briinn 




139-5 





Egisheim, Stangenas, Dschagga negroes, Veddahs, and Kalmucks absent. 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 151 



Table VIII. — Comparison oe the Frontal Angle. 





Minimum. 


Average. 


Maximum. 


1. Pithecanthropus erectus .... 




52*5 




2. An adult male chimpanzee 




56 




3. Three Spy-Neandertal .... 


57-5 


64-8 


70 


4. Gibraltar ...... 




73 




5. Briix . 




74-7 




6. Briinn ....... 




75 




7. Galley Hill 




82 




8. Cro-Magnon ...... 




83 




9. Four Kalmucks ..... 


80 


85-2 


91 


10. One hundred Australians, unsexed . 


71 


85-2 


100 


11. Forty-four Tasmanians, unsexed 


72 


86 


96 


12. Egisheim 




89 




13. Stangenas 




92-5 




14. Forty Europeans, unsexed 


73 


92-5 


103 


15. Twenty-four Dschagga negroes 


88 


100-3 


110 



Veddahs absent. 



Table IX. — Comparison of the Bregma Foot-Point Positional Index. 





Minimum. 


Average. 


Maximum. 


1. An adult male gibbon .... 




63-4 




2. Pithecanthropus erectus .... 


39-7 


44-1 


50-2 


3. Stangenas ...... 




38-9 




4. Briix ....... 




37-3 




5. Three Spy-Neandertal .... 


34-8 


36-6 


40-1 


6. Gibraltar ...... 




35-2 




7. Galley Hill 




34-3 




8. One hundred Australians, unsexed 


29-2 


34-1 


38-8 


9. Briinn 


. . 


34 




10. Forty-four Tasmanians, unsexed 


26 


33-5 


40-6 


11. Egisheim ...... 




33-3 




12. Four Kalmucks 


30-1 


32-8 


37-4 


13. Cro-Magnon 




32-6 




14. Twenty-four Dschagga negroes 


26-6 


32-1 


37-2 


15. Forty-five Europeans, unsexed 


22-2 


30-4 


35-7 



Veddahs absent. 



152 



Proceedings of the Poyal Society of Edinburgh. [Sess. 



Table X. — Comparison oe the Lambda Angle, 





Minimum. 


Average. 


Maximum. 


1. Nearest anthropoids .... 


43 


55-5 


68 


2. Pithecanthropus erectus .... 




66 




3. Neandertal ...... 




66*5 


67 


Spy i 


67 


68 




4. Gibraltar ...... 




69 




5. Cro-Magnon ...... 




70 




6. Galley Hill 




74 




7. Briinn ....... 




78 




8. One hundred Australians, unsexed . 


70 


79*5 


90 


9. Briix ....... 




80 




10. Forty-six Tasmanians, unsexed 


74 


80-5 


88 


11. Stangenas ...... 




81-5 




12. Modern Man . . . . 


78 


81-5 


85 



Egisheim, Dschagga negroes, Veddahs, and Kalmucks absent. 



Table XI. — Comparison of the Opisthionic Angle. 





Minimum. 


Average. 


Maximum. 


1. Pithecanthropus erectus .... 




64 




2. Nearest anthropoids .... 


50 


59*5 


69 


3. Spy 1 




54 




Neandertal 




51-5 




4. Galley Hill 




42 




5. Briinn 




42 




6. Thirty-eight Tasmanians, unsexed . 


34-5 


40-6 


47 


7. One hundred Australians, unsexed 


31 


40 


51-5 


8. Gibraltar 




36 




9. Recent Man ...... 


31 


35-5 


40 


10. Cro-Magnon ...... 




34 





Egisheim, Stangenas, Briix, Dschagga negroes, Veddahs, and Kalmucks absent. 



Table XII. — Comparison of the Length of the Frontal Arc. 





Minimum. 


Average. 


Maximum. 


1. An adult male chimpanzee 




92 




2. Pithecanthropus erectus .... 


100 


110 


120 


3. Four Kalmucks 


110 


115-2 


120 


4. Three Spy-Neandertal .... 


115 


124 


133 


5. Seventeen Maories, unsexed . 


116 


125 


135 


6. Five Europeans, unsexed 


121 


125-6 


130 


7. Forty-seven Tasmanians, unsexed . 


113 


126 


143 


8. Gibraltar 




126 




9. One hundred Australians, unsexed . 


116 


126-8 


143 


10. Briix 




135 




11. Galley Hill ...... 




135 




12. Briinn 




135 




13. Cro-Magnon 




138 





Egisheim, Stangenas, Dschagga negroes, and Veddahs absent. 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 153 



Table XIII. — Comparison of the Length of the Chord of the Pars 
Cerebralis of the Os Frontale. 





Minimum. 


Average. 


Maximum. 


1. An adult female chimpanzee and a gibbon 




55 




2. Gibraltar ...... 




82 




3. Spy-Neandertal ..... 


77 


83-6 


87 


4. Pithecanthropus erectus .... 


80 


87-5 


95 


5. Eleven Europeans, unsexed 


87 


92-1 


101 


6. Fifty Tasmanians, unsexed 


73 


93-7 


106-5 


7. Galley Hill 




95 




8. Five Dschagga negroes .... 


94 


95-8 


97 


9. One hundred Australians, unsexed . 


85 


95-9 


112 


10. Briinn ....... 




96 




11. Cro-Magnon ...... 




97-5 




12. Briix 




99 





Egisheim, Stangenas, Kalmucks, and Veddahs absent. 



Table XIV. — Comparison of the Length of the Chord of the Os Frontale. 





Minimum. 


Average. 


Maximum. 


1. An adult male chimpanzee 




87 




2. Four Kalmucks 


98 


103-8 


107-5 


3. Pithecanthropus erectus .... 


96 


104 


112 


4. Fifty Tasmanians, unsexed 


97 


109-5 


120 


5. Seventeen Maories, unsexed . 


103 


110 


119 


6. One hundred Australians, unsexed . 


100 


110-8 


124 


7. Gibraltar 




111 




8. Five Europeans, unsexed 


109 


112-5 


118-5 


9. Three Spy-Neandertal .... 


108 


114 


119 


10. Briix 




114 




11. Galley Hill ...... 




120 




12. Briinn ....... 




123 




13. Cro-Magnon ...... 




123 





Egisheim, Stangenas, Dschagga negroes, and Veddahs absent. 



Table XV. — Comparison of the Parietal Frontal Arc Index. 





Minimum. 


Average. 


Maximum. 


1. Briix ...... 




80 




2. An adult female chimpanzee . 




82-6 




3. Pithecanthropus erectus .... 


71-1 


85-8 


102-7 


4. Gibraltar. ...... 




88 




5. Seventeen Mariories, unsexed . 


81 


93-3 


104 


6. Three Spy-Neandertal .... 


89-4 


96-8 


104-3 


7. Galley Hill 




97-7 




8. Cro-Magnon 




97-8 




9. One hundred Australians, unsexed . 


87-7 


99-3 


113-9 


10. Forty-five Tasmanians, unsexed 


85-8 


99-7 


114-1 


11. Briinn ....... 




103-3 




12. One European ..... 




109-9 





Egisheim, Stangenas, Dschagga negroes, Veddahs, and Kalmucks absent. 



154 



Proceedings of the Royal Society of Edinburgh. [Sess. 



Table XVI. — Comparison of the Distance of the Bregma Foot-Point 
from the Glabella. 





Minimum. 


Average. 


Maximum. 


1. Pithecanthropus erectus .... 


72 


81-5 


91 


2. Briix ....... 




75 




3. Three Spy-Neandertal .... 


67 


72-3 


81 


4. An adult male chimpanzee 




72 




5. Galley Hill 




69 




6. Briinn ....... 




67-5 




7. Gibraltar ...... 




66 




8. Cro-Magnon ...... 




66 




9. One hundred Australians, unsexed 


51-5 


61-2 


74 


10. Forty-four Tasmanians, unsexed 


45 


58-7 


71-5 


11. Four Kalmucks ..... 


51-5 


54*6 


61 


12. Twenty-four Dschagga negroes 


41 


53-9 


62-5 


13. Thirty-five Europeans, unsexed 


40 


51-3 


61 



Egisheim, Stangenas, and Veddahs absent. 



Table XVII. — Comparison of the Length of the Parietal Chord. 





Minimum. 


Average. 


Maximum. 


1. Briix ....... 




100-5 




2. Pithecanthropus erectus .... 




104 




3. Seventeen Maories, unsexed . 


92 


104 


110 


4. Three Spy-Neandertal .... 


104 


107-7 


113 


5. Gibraltar ...... 




108 




6. Forty-eight Tasmanians, unsexed . 


99-5 


113 


127 


7. One hundred Australians, unsexed . 


98 


114-6 


137 


8. Galley Hill 




120 




9. Cro-Magnon ...... 




123 




10. Briinn ....... 




127-5 





Anthropoids, Egisheim, Stangenas, Dschagga negroes, Veddahs, Kalmucks, 
and Europeans absent. 



Table XVIII. — Comparison of the Curvature Index of the Os Frontale. 





Minimum. 


Average. 


Maximum. 


1. Pithecanthropus erectus .... 


93-3 


94-6 


96 


2. An adult male chimpanzee 




94-5 




3. Three Spy-Neandertal .... 


89-4 


92-8 


93-9 


4. Briinn ....... 




91-1 




5. Four Kalmucks ..... 


88-3 


90-1 


92-8 


6. Five Europeans, unsexed 


87-4 


89-5 


91-1 


7. Cro-Magnon ...... 




89-1 




8. Galley Hill 




88-8 




9. Gibraltar ...... 




88 




10. One hundred Australians, unsexed . 


81-3 


87-4 


90-8 


11. Forty- seven Tasmanians, unsexed . 


81-4 


87-1 


97-5 


12. Stangenas ...... 




85-2 




13. Briix 




84-4 





Egisheim, Dschagga negroes, and Veddahs absent. 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 155 



Table XIX. — Comparison of the Distance of the Foot-Point of the 
Calvarial Height from the Glabella. 



1. Pithecanthropus erectus 

2. An adult male gorilla 

3. Four Kalmucks 

4. Forty- one Europeans, unsexed 

5. One hundred Australians, unsexed 

6. Forty-five Tasmanians, unsexed 

7. Gibraltar .... 

8. Briinn ..... 

9. Three Spy-Neandertal 

10. Briix 

11. Galley Hill .... 

12. Cro-Magnon .... 



Minimum. 


Average. 


Maximum. 


70 


80*5 


91 




84 




76 


86-3 


95 


78 


95-8 


112-5 


88 


101-1 


123 


85 


101-9 


115-5 




105-7 






110 




103 


111 


123 




111 






111 






121-5 





Egisheim, Stangenas, Dschagga negroes, and Veddahs absent. 



Table XX. — Comparison of the Glabella-Cerebral Chord Index. 





| Minimum. 


Average. 


Maximum. 


1. Gibraltar 




43 




2. An adult female orang .... 




40 




3. Three Spy-Neandertal .... 


34-4 


39-6 


43-1 


4. Cro-Magnon 




32-3 




5. Briinn ....... 




31-2 




6. Pithecanthropus erectus .... 


25-2 


27-6 


30 


7. Egisheim ... . . 




27-5 




8. Five Dschagga negroes .... 


23-3 


27-4 


30-3 


9. Eleven Europeans, unsexed 


21-4 


26-6 


31-8 


10. Fifty Tasmanians, unsexed 


17-6 


25-5 


35-6 


11. Galley Hill 




25-2 




12. Briix 




24-2 




13. One hundred Australians, unsexed . 


15-6 


23-6 


33-5 


14. Stangenas ...... 


•* 

i 


18-6 





Kalmucks and Veddahs absent. 



156 



Proceedings of the Royal Society of Edinburgh. [Sess, 



Table XXI. — Comparison of the Maximum Breadth. 



1 


| 

Minimum. 


Average. 


Maximum. 


1. An adult male chimpanzee 


.. 


113 




2. Four Veddahs ..... 


123 


129-7 


135 


3. Briix . 




130 




4. Galley Hill 




130 




5. One hundred Australians, unsexed . 


120 


130-7 


143 


6. Pithecanthropus erectus .... 




133 




7. Nineteen Andamanese Islanders, unsexed 


128 


133 


141 


8. Forty-eight Tasmanians, unsexed . 


120 


134-7 


145 


9. Fifteen Maories, unsexed 


128 


136 


141 


10. Briinn ....... 




139 




11. Five Europeans (Germans), unsexed . 


137 


142-4 


149 


12. Ninety Europeans (Italians), unsexed 


124 


142-5 


155 


13. One hundred and seventy-six Europeans 








(Scotch), unsexed .... 


128 


143-6 


159 


14. Four Kalmucks ..... 


140 


146 


148 


15. Gibraltar ...... 




148 




16. Three Spy-Neandertal .... 


146 


150-3 


153 


17. Cro-Magnon ..... 




151 





Egisheim, Stangenas, and Dschagga negroes absent. 



Table XXII. — Comparison of the Curvature Index of the Os Parietale. 





Minimum. 


Average. 


Maximum. 


1. Gibraltar ...... 




97-2 




2. Three Spy-Neandertal .... 


90-4 


93-7 


96-3 


3. Briix 




93 




4. Pithecanthropus erectus . . . 




92? 




5. Briinn ....... 




91-3 




6. Cro-Magnon ...... 




91-1 




7. One hundred Australians, unsexed . 


81-6 


91 


103-6 


8. Galley Hill 




90-9 




9. Forty-seven Tasmanians, unsexed 


83-8 


90 


97-6 



Anthropoids, Egisheim, Stangenas, Dschagga negroes, V eddahs, Kalmucks, 
and Europeans absent. 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 157 



Table XXIII. — Comparison of half the Sum of the Glabella -Inion Length 

plus the Breadth. 





Minimum. 


Average. 


Maximum. 


1. An adult female gorilla .... 




129 




2. Four Veddahs 


142-5 


149-5 


153-5 


3. Forty-four Tasmanians, unsexed 


140-5 


154 


164-5 


4. Four Kalmucks ..... 


148-5 


154-3 


161 


5. Briix 




155 


157-5 


6. One hundred Australians, unsexed . 


143 


155-05 


166 


7. Five Europeans, unsexed 


153 


156-8 


159 


8. Pithecanthropus erectus .... 




157 




9. Galley Hill 




165-5 




10. Gibraltar ...... 




167-5 




11. Briinn ....... 




170 




12. Three Spy-Neandertal .... 


172 


174-3 


177 


13. Cro-Magnon 

1 




176-5 





Egisheim, Stangenas, and Dschagga negroes absent. 



Table XXIV. — Comparison of the Calvarial Height Foot-Point 
Positional Index. 





Minimum. 


Average. 


Maximum. 


1. Pithecanthropus erectus .... 


38-6 


44-4 


50-2 


2. Four Kalmucks ..... 


43-6 


52-6 


56-8 


3. Briinn ....... 




54-7 


• • 


4. Galley Hill 




55-2 




5. Three Spy-Neandertal .... 


52 


55-7 


60-8 


6. Forty-one Europeans, unsexed 


48-8 


56-2 


66-9 


7. One hundred Australians, unsexed . 


44-8 


56-3 


65-3 


8. Gibraltar 




56-5 




9. Forty-four Tasmanians, unsexed 


53-1 


59 


64-8 


10. Briix 




60(61-6) 




11. Cro-Magnon . . 




60-1 




12. An adult female gorilla .... 




61-8 





Egisheim, Stangenas, Dschagga negroes, and Veddahs absent. 



158 



Proceedings of the Royal Society of Edinburgh. [Sess. 



Table XXV. — Comparison oe the Glabella -Inion Length. 





Minimum. 


Average. 


Maximum. 


1. An adult male gorilla .... 




147 




2. Four Kalmucks 


157 


166-2 


174 


3. Twenty- three Dschagga negroes 


145 


167-4 


180 


4. Thirty-one Europeans, unsexed 


155 


168 


184 


4. One hundred and fifty-four Europeans, 








unsexed ...... 


154 


169-3 


199 


5. Eight Veddahs ..... 


160 


169-8 


176 


6. Forty-four Tasmanians, unsexed 


157 


173-1 


188 


7. One hundred Australians, unsexed . 


162 


179-5 


196 


8. Pithecanthropus erectus .... 




181 




9. Briix 




185 (180) 




10. Gibraltar ...... 




187 




11. Three Spy-Xeandertal .... 


196 


198-6 


202 


12. Galley Hill ...... 




201 




13. Briinn 




201 




14. Cro-Magnon 




202 





Egisheim and Stangenas absent. 



Table XXVI. — Comparison of the Length of the Chord of the 
Pars Glabella of the Os Frontale, 





Minimum. 


Average. 


Maximum. 


1. An adult female orang .... 




20 




2. One hundred Australians, unsexed . 


15 


22-3 


29-5 


3. Forty-nine Tasmanians, unsexed 


18 


23-8 


29 


4. Pithecanthropus erectus .... 




24 




5. Briix 




24 




6. Galley Hill 




24 




7. Eleven Europeans, unsexed 


19-5 


24-5 


28 


8. Five Dschagga negroes .... 


27 


26-4 


28-5 


9. Briinn 




30 




10. Cro-Magnon 




31-5 




11. Three Spy-Neandertal .... 


30 


33-1 


37-5 


12. Gibraltar ...... 




36 


•* 



Egisheim, Stangenas, Kalmucks, and Veddahs absent. 



Table XXVII. — Comparison of the Angle of Parietal Curvature. 





Minimum. 


Average. 


Maximum. 


1. Pithecanthropus erectus .... 




150 




2. Chimpanzee ...... 




149 




3. Three Spy-Neandertal .... 


142-5 


142-6 


143 


4. Galley Hill 




139 




5. One hundred Australians, unsexed . 


125 


135-7 


145 


6. Briinn ....... 




135 




7. Forty-nine Tasmanians, unsexed 


125-5 


134-3 


141-5 


8. Cro-Magnon old man .... 




134 




9. One European (Schwalbe) 




129 





Gibraltar, Briix, Kalmucks, Veddahs, Dschagga negroes, Egisheim, 
and Stangenas absent. 



Pm Boy.. Sots. Min., [Vol. XXXIV.] 



Table XXVIII.— THE INDIVIDUAL AND GENERALISED RESULTS OE THE EXAMINATION • OF ONE HUNDRED AUSTRALIAN CRANIA. 



i Roberson Serial Nuvil 



III 



21 22 23 



35 \ 36 I 37 



f IBBe 



| 66 | 67 | 62 | 63 | 


64 | 65 | 66 | 67 | 63 ] 69 | 


mm\ 


■ | 


73 I 74 | 75 [ 76 | 77 j 7 


8 


79 | 40 ' I 37 | 82 | S3 j 34 j 35 "j 36. | 37 | SS j 39 | 96 | 97 j 92 | 93 | 94 | 95 | 96 | 97 | 93 j 96 j 100 


No. 


Hi,,. 


O 


Max. 




















Natioi 




I'SEUM, 


Melbourne. 














































. 12999 


12991 


12980 


12960a 


| 12736 


12724 




12968] 


12967 1 12966 1 


12975 


12965 


12987 


12988 


13018a 

M. 


12974 

F. {!’ 


F. 


12837 

M. 


1 


I. 


'isoosa 


|13010a 

' 


12970 


| 13002 |l3003A 


13004a 


12977 


12978 


12981 




12822 


12963 


129C4 




12986 


12925 


12973 


13027 




12739 




12982 


s 








| m 


173 


176 


17S 


I 187 


175 




174 








178 


180 | 




167 




171 


173 


•5 


llso 




186 


191 


182 


191. | 




177 




173 


193 




184 


188 


176 


187 


181 


181 


177 


173 


169 


177 


100 


102 


179-61 


190 


1.166 


169 


169 


171 1 




171 ■ 


184 


168 


177 Il62 


170 


181 


171 


177 


177 


163 


166 


165 


170 




jl73 | 


182 


178 ' j 


187 


180 


185 | 


177 


172 


167 


.107 I 


H 


170 I 


180 


187 


172 


179 | 


177 


17% 1 -j 


172 


&■ 


104 


170 


100 




173-84 


191 


| 93-5 


102-5 


95 


97 j 


| 95 


95 


103-5 | 


99 


93 90 


92 


92-5 j 


98 


93-5 


91 


'89 | 


82 


88 j 


89 




1*96-5 


96-5 


103 


lOO'o- 


86-5 


94 


93-5 


91 


88 


92-6 


99 


IB 


93 


99 


90-5 | 


93-6 


94.5 j 


97-5 


03. 


160 


89-6 


91 j 


100 


79-5 


B 


108 


| 54-36 


ba 

120 


54-28 


54-49 


| 56-34 | 

B 


54-28 


54-47 


56-89 


pZp%| 54-87 


52-27 


50-00 


55-05 


51-94 


49-86 


53-29 


48-80 


51-46 


51-58 


[53-67 


51-05 


55-37 


52-61 


47-52 


49-22 


51-51 


51-41 


51-46 


53-46 


51-29 


50-57 


50-54 


52-65 


51-42 


50-00 


52-20 


53-86 


52-54 


57-80 1 


52-95 


51-41 


100 


44-91 


63-00 


61-53 


129 1 




128 


134 122 | 


129 


130 | 


128 


jl32 


127 


132 


136 


124 


125 




36 


128 


131 


136 


134 


129 


134 | 


125 


127 


123 


135 


121 


133 


136 


133 


131 


3.31 


133 


128 


135 


131 


127 


100 


MM 


130-71; 


143 






















































































ion 


60-29 


72-70 


85-41 


Il51 


146-5 


152 


154-5 


157 


152 


163 


151 


157-5 


143 


152-5 


157-5 


153 


156 


154-75 


149-5 


152 


147-5 


149 


-25: 


158 


158-6 


158-5 


163-5 


158 


160 


157-76 


161 


149 


148 


164 


147-6 


jttl I 


162 


154-5 


159 


156 


166 


162-6 


154 


160 ■ 


152 


100 '1 


143 


155-05 


166 






62-50 


62-73j 




62-56 


63-49 


65-56 


59-04 


62-93 


00-52 


53-73 


64-65 


59-93 


-68 80 


59-53 


53-94 


59-66 


59-96 


67-67 


66-33 


64-98 


61-46 


54-74 


58-75 


59-27 


66-26 


50-00 ■ 


62-56 


60-36 


59-66 


58-67 


m 


58-57 


58-80 


' 60-57 


62-50 


00-03, 


64-93 


59-66 


B 


100 


52-30 


61-32 


09-95 


94 


101 


104 


93 


|ll3 


105 


106 


103 


104 


91 


95 


108 


100 


99 


93' 


103 


95 


99 


92 




96-5 


106 


98 


101 


96-5 


in 


99 


105 


108-5 


97 


111 


97 


103 


94-5 




109 


96-5 


92-5 


101 


01-6 


04 


100 


100 


88 


101-11 


123 


54-65 


53-33 


59-42 


52-2i[ 


j 66-42 


66-66 


55-78 


59-79 


57-45 


55-48 


53-97 


58-37 


56-17 


55-00 


50-95 


61-67 


56-54 


.57-89 j 


0-31 


55-27 


56-08 


52-68 


52-87 


53-02 


58-11 


54-54 


59-32 


63-45 


50-00 


57-51 


.55-74 


55-97 


50-26 


53-69 


58-28 


53-31 


51-10' 


57-06 


52-88 


55-62 


56-49 


100 


44-80 


56-36 


05-31 


91 


93 


95-5 


80-5 j 


79-5 


92 


; 89 • 


97-5 


90 


89 


80 


83-5 


83 


82 


80 


92 


90 


79 


9(j 




80 


90 


86-5 


89-6 


77-5 


77- | 


85 - 


95 


87 


83 


79 . 


83 


76 


94 


84 


72 


80 . 


90 


79 


82 


06 


78 


100 


Bl 


85-21 


1 : ■> 


1 56-5 


60 


51-5 


55-5 | 


54-5 


56 


56 


56 




55 


53. 


52 


56 


55 


53-5 


53-5 


63 


53 


64 


-5 


66. 


54-5 


57-5 


57 


50 


61 


52 


53 


52 


53 


52 


53 


52 


55 


53-5 


52-5 


64 


64 


53 


69 


64 




gw 


49 


54-77 


60 


54 


54-5 


56 


62 ! 


58-5 


69 


61 


62 


59 


58 


63 


65-5 


59 


58 


63 


60 


59 


60 


59 




63 


63 


61 


59 


69 


71-5 


68 


61-5 


63 


64 


67-5 


59 


71-6 


64 


61-6 


63 


u . 


; 66 


65 


66-5 


60-5 


66 


100 


51-5 


'61-26 


74 


31-39 


37-56 


32-00 


54-53! 


37-23 


33-77 


32-10 


35-63 


32-59 


35-36 


35-79 


35-40 


33-14 


52-22 


34-52 


35-92 


35-11 


35-08 


34-00 


35-00 


33-33 


32-84 


30-89 


37-91 


37-43 


37-46 


34-74 


36-84 


30-00 


34-97 


33-90 


33-35 


34-04 


34-94 


33-68 


35-91 


35-91 


30-721 


32-65 


35-79 


37-28 


100 


- 29-21 


34-12 


38-86 


167 


177 


176 


178 1 


P 85 


77 


189 


181 




167 


176 


182 


178 


175 


180 


168 


164 


170 


171' 




180 


182 


186 


184 


174 


189 | 


180 


176 


172 


176 


194 


168 


181 


185 




187 


J/7 


180 


179 


178 


170 


174 


100 


161 


jUi 


194 


17 


20 


18 


16-5 


16 


| 14-5 


20 


ifT 


17-5 


15-5 


13-5 


17-5 


16-5 


16-5 


15 


15-5 


15-5 


16 


m 




18 ! 


16 


17 


19 


15-5 


16 


16 


19 


16 


15-6 


pM 


16-5 


16-6 


17 


16-6 


16 


16 


13-5 


mo 


2° 


18 


17-5 


mu 


13-5 


16-99 


22-5 


76 


83-5 


80 


85 | 


79 


78-5 


88 


84-5 


82-5 


79 


81 


88 


87 


80-5 


82 


80 


•77 


81 


78 




88 


83:5 


87 


85 


89 


91-5 


89 


85 


83 


85 


90 


80 


88-6 


88-5 


82 


: 84-5 


88 


86 


87 


84 


84 


89 


100 


73 


85-33 


101%-! 


45-50 


47-17 


45-45 


47-75 


42-70 


44-35 


46-56 


46-68 


46-67 


47-30 


46-02 


48-34 


48-87 


46-66 


45-55 


47-61 


46-95 


47-64 


45 


■61 


48-88 


45-87 


46-77 


46-19 


51-14 


48-41 


49-44 


43-29 


48-25 


43-57 


1-46-39 


47-61 


43-39 


47-83 


47-12 


45-13- 


49-71 


47-22 


; 48-60 


47-19 


49-41 


61-14 


100 


40-95 


47-20 


53-16 


122 


|l26 


127 


126 | 


|f25 


129 


129 


142 


124 


125 


125 


127 


131 | 


120 


122 


125 


116 


120 


123 




131 


128 


134 ■ 


128 


125 


133 


132 


123 


124 


125 


131 


118 


124 


137 


124- 




127 


136 


S|[||j 


125 


L25 


125 


100 : 


I III 


126-84 


143 


106-5 


112-5 


109 


112 


107 | 


109 


113 


115-5 


108-5 


108-5 


110 


111 


115 


109 


108-5 


105-5 


101 


105 


106 




III 


107 


119 


113-5 


112-5 


118 


114 


105 


107 


110 


115 


105 


112 


116 ; 


rjgjg 


108 


116 | 


116 


112-5 


114 


108 


no 


100 : 




110-87 


124-5 


37-20 


39-23 


85-82 


55-55! 


85-60 \ 


34-49 


87-59 


81-33 


87-50 


50-50 


55-00 


87-40 


37-73 


90-83 


S8-93 


84-40 


87-06 


87-50 


s«! 


■ii\ 


34.73 


33-59 


88-80 


88-67 


00-00 


88-72 


36-36 


85-36 


36-29 


8S-00 


37-73 


33-93 


96-32 


84-67 


87-09 


89-25 


90-55 


85-29 


88-58 


91-20 


86-20 


88-00 


.100 


81-30 


87-43 


90-83 


137 


138 


131-5 


144-5 


;|l4l-5 


133 


142 


126 


136 


135 


139 


139 


140 


146 


143 


139 


J.34 


143 








138 


140 


137 


146 


145 


140 


132 


137 


140 


144 


139 


144-5 


136 


jffpgj 


149-5 


142 


134 . 


140 


142 


140 


H 


100 


123-5 


L39-65 




24 


26 


20 


20-5 ; 


27-5 


20 


24-5 


21 


21 


22 


25 


22 


pp 


21-5 ! 


24 


20 


21 


27 






25 


21-5 


27 


18-5 


21-6 


25 


21-5 


.18 


24 


21-6 


24-5 


20 


21-6 


22 


19:5 


26 


21-5' 


26-6 


24 


21-5 


24 


25 


100 


15 


22-36 


29-5 


90 


94 


96-5 


98 


87-5 


96 


98-5 


102-5 


94 


91 


92 


96 


100 


93 


91-5 


93-5 


87 




96 




98 


98 


100 


100-5 


98 


100 


101 


95 


94 


97 


99 


91-6 


96-6 


P I 


94-6 


88-5 


100 


100;5 


96 


96-5 


94-5 


93 


100 


85 


95-08 




| 26-66 


27-65 


20-72 


20-91 


| 37-42 


26-33 


24-37 j 


20-48 


22-34 


24-17 


27-77 1 


22-91 


22-66 


23-11 1 20-22 


21-39 


24-13 


31-03 




,2 


25-51 


27-93 27-66 


18-40 


21-93 


25-00 


21-28 


18-94 


23-40 


22>16 


24-74 


21-85 


22-27 


21-15 


20-63 


29-37. 


21-50 


20-30 25-00 


22-27 


25-39 


26-88 


[ : :Wj 


16-02 


23-60 


33-62 


124 


130 


112 


127 


134 


134 


136 I 


137 


124 


121 


130 


119 


126 


126 


128 


120 


114 


ns 


126 




124 


133 


137 


142 


113 


127 


124 , 


114 


agn 


122 


130 


120 


122 


mu 


124 


132 


125 


132 




BH 


114 


113. 


100 


109 


126-91 


L'47: I ' 


110 


117 


116 


114-5 


122 H 


120 


119-5 


122 


114 


110 


116 


111 


114 


114 


117 


108 


105 


108-5 


113; 




113-5 | 


ii9 . 


124 


119 


104 


117-5 


IB 


105-5 


107 . 


110-5 


122 


108 


112-5 


BB 


111-5 


119 


iil -5 


119 


112 


116 


106 


104." 


100 


98 


114-60 


137 


88-70 


90-00 


103-57 


90-15 


91-04 


I 89-55 


57-55 


89-05 


91-93 


90-90 


39-23 


93-27 


90-47 


S0-47\ 91-40 i 


,00-00 


92-10 


91-94 


: 89-68 


91-53 


89-47 




83-80 


92-03 


92-51 


89-91 


92-54 


93-04 


90-57 


93-84 


Wsi 


92-21 


12 


30-01 


90-15 


- 


90-15 


92-56 


85-29 


92-98 


92-03 


100 


8i-66' 


ISMS 


103-07 


|132 


131 


135 


134 


[133-5 


129 


|l34 


132-5 


|l36-5 


®fr 


|l35 : ! 


136 


137 


134 |l38 


132 


139 136-5 132 




137-5 


132 


136 j 


136 | 


140 


138 136 | 


|M 


134 


137 


137 


134 


138 


137 |137 ; 


134 


133 


m - 


140 


138 


141 


137 


100 


126 


135-77 


145 


\l01-63 


763-77 


88-18 


766-70 


767-26 


763-37 


765-42 


| 96-47 


766-66 


96-80 


104-00 


I 93-70 


96-18 


165-66 764-91 96-66 


| 93-27 1 98-33 ]l62 


■43] 


94-65 


|j63-96 


102-23 | 


. 


lift 


95-48 j 93-93 


92-68 


92-74 


97-66 


99-23 


101-69 


98-38 


95 cz\^^ 


|®0 


98-42 


97-65 


95-27 


108-80 


91-20 


96-46 


100 


IB 


99-32 


113-90 


76 


84 


83 


80 


76 


[84 


77 


!>0 | 


76 


84 


82 


75.5 


79 


75 [83 


78 


m 77 


79 




78 


74 - 


81 


73 


, 70 


70 


78 


IW 


81 


82 


81 


74 


77 


78 


Mi 


.80 


IB 


.80 


81 


83 


81 


(H 


100 


70 


79-56 


90 


45 


38 


34 


37 


40 


34 


31 


33 


38 


43 


46-5 


I 48 


38 


45 | 


39 


45 | 41 


42 




41 


'ISfl 


35 


38-5 


43 


41 


34-5 


39 


38 


38 


38 


41 


49-5 


39 


41 


42 


42 


35 


44 


M 1 


35 


45 


m 


1 31 


40-06 


51-5 



Present Location of :Specim 



University, Melbou: 



Original Number of Special 



M. M. M. M. M. 



8 11 II 12 I 13 



12989 13006a 12995 



13026 



Glabella-Inion Length*, 



Nasio-Inion Length. 



Calvarial Height. 



190 



159 171 171 



94-5 96 108' 



172 170 174 



52-87\ 52' 



48-6S 53-24 



54-31 \ 54-54\ 60-67 \ 54-46 1 55-55 55-05 



4 Maximum Breadth. 



137' 136 137 137 



50-57 51-42 56-33 
32 |l23 |l2S 



mnigam of Glabella-Inion Length - 



70-93 69-54\ 77-55 75-55 73 



35 69-OS 70-541 72-69 79-33 



3-57] : 



148-5 157-5 164-5 



166 153-5 149-5 



57-27 63-14 1 64-77 62 



22 56-21 61-60 62-17 64-641 63-5 



9-34 57-65 



60-53\ 65-46 



right Boob-Point from Glabella. 



1-10 1 58-37 56-52 57 



90-5 107 



56-54 1 54-21 58-04 51-42 \ 60-11 54-92 1 59-4 



52-80\ 61-66 



63-40 57-45 



5 71 85 



88 88 . 86 



50 55 54 



57-5 55 5' 



Distance of Bregma Foot-1 



■1 






75 37-17 32-53 34-48 33-6 



Glabella -Lambda Length. 
Lambda-G34holla-Inion Angle. 



1-89 \ 34-19 33-8 



161 172 176 



17 16 21 



Distance of Bregma Foot-Poin 



a Glabella on Glabella-Lambda Lin< 



46-17 41-34 



49-19 50-26 47-82 48-25 



M^nPh^&fjFrontal Chord. 



16-5 116 106 



121 114 



87-39 \ 90-33 87-40 



Angle of Frontal Curvature. 



Length of Chord of Pars Glabellaris. 



ngtli of Chord of Pars Cerebralis 



150 143 136 



29 26-5 22-5 15-5 



Length of Parietal Arc. 



Length of Parietal C 



54 1 26-63 27-53 27-36 27-37 25-73 75-30 76-47 



)-79 23-36 < 



129 121 110 



96-24 1 ! 



92-66 i mm 



vAh'gle. of Parietal Curvature. . 



R. J. A. Berry and *Di§/A. W. D. Robertson. 



89-34 1 102-9 



J137 |l 36 1 145 |l31-5 |lS 



127 133 134 



55-37 94-24 



76-5 75 77 



40 43 39 































V 
















Table XXIX. 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 159 



Stangenas. 


14-62 

| 8-64 
11-21 

10-79 

8- 84 

9- 66 

7-79 

7-18 


78-73 


91-69 


•8586 


Briinn. 


CD !>OT)(^COI>rHCDlC<N^M(NC5'cHOCOQO©JOQOeO<M® 
OO ;^OCpr^r-lOcpcOI>'Cp'>^COQpoOcpC5l^'THt^Cit^OT)HOJ 
cb <©©d5Gbd5cb©c©i©c©c©c©»ocb»ocb4<cbcbcb'iHiOTH 

r— 1 iH iH 


166-94 


co 

oq 

© 

oq 


•7755 


Cro-Magnon. 


lO WOOOlMlOCOtNOJ^lMlOCOlOHODNlOOCOilOOffiN 
CO ;oW©-f©NHWG0NN©^Mt^l0»0Hl0O>0i01>iy| 

cb G©©cbi^cbc»HibiAd5cbcb^^^^cbcbiocbiOHio^ 


168-21 


215-23 


1 — 1 
00 


Egisheim. 


13-09 

11-80 

11-70 

9-8*5 

10-86 

4-56 

2-69 


64-55 


78-57 


•8215 


Dschagga 

Negroes. 


1 13-09 
57-6 

i 12-15 
14-07 

12-90 

11-30 

8-40 

7-68 

4-59 


89-94 


96-80 


© 
1 oq 

05 


Europeans. 


bt'OOt'tOHDHCDiOCC^HNO CO CD CO t" 00 © 

0®ffiOiOQO'#t^q5CO'^I>COHTt<^ ] ©q rf< OO CO ‘(MrHCD ; 

cb^©cb-^©cb©H©i^cbi>cbi^db 4i cb ^-h -cH cb h 


178-25 


206-79 


© 

oq 

© 

00 


Veddahs. 


12- 89 
11-41 

13- 30 
11-17 

2-42 

2-39 


53-58 


62-31 


•8598 


Tasmanians. 


CO>0-^>OCO'^iO'^®®(NHl>0(M-^HHCO»0'<iM>(MI>OOH 

coHaoco©i^io©i^c^Hao©^©coco©q''cHHHio©'i^©<©q 

cb-^05©cb©i^o5©©cocoiAiO'i^cbcbcbcbiocbcbcb'-Hio-^H 


172-36 


© 

05 

© 

cq 

oq 


oo 

© 

t-* 


Galley Hill. 


CO T)(lO®t'DOOOO , 0(NCOH(MQOI>OD'^©COiO®OOH 

co ;cpcococow9>9Qpj>Diu9^THoaocoM'^H(cioc»'^ 
cb ocbi^'^cot^ocoiococbiA'^cb'^'cHThiocbcb^HrHcb'^ 


154-24 


co 

oq 

i s 

1 oq 


•7166 


Australians. 


CKMHOCOODCOOOHt^TjKMOMO^t^OHCDOO^DaD 
OOHOOCOOiOOOi005Clffl-ft^QOcp®OCOI>lOOOHH^ 
; p^^odiodii^cbocbcDcbco^-^iocbiocbiocbcbcbrHiorli 


163-39 


220-99 


1 co 
© 
co 
c- 


Kalmucks. 


10-73 

6- 85 

10- 94 

11- 15 
8-02 

8-83 

11-04 

4-65 

4-02 

7- 48 

3-73 

0-93 

I 4-78 

2-95 
| 0-82 


96-92 


lO 

© 

cb 


•6775 


Spy- 

Neandertal. 


DiOCODOOH(N(Ml>OOHHDl>ODO©DOO^XCOa)'cH 

COCODI>(»'7iCOCOCOOCO'^CO'^CqiOiO^OOO'^l^C5rHDI> 

dsrH^ioio-^cDcbdi^cbcDOcb-^cbi-Hr-H^rHibf-HiOrHcbcb 


111-57 


220-99 


•5049 


Briix. 


ao lOCODDiOONH ©q © t- h lO © ^ ® ffi CO 1> © 

©q ;ooooco^n-^Oi^i— i ,coof oo ^ooio^ooio ; © 

ds Ai^i^©io*b©© cb©co©H©cb4i©cbcbcb>H 'cb 


124-43 


© 

t" 

05 

© 

oq 


•5931 


Gibraltar. 


00 NffilCCOOCOI>HNHCD100HCDI>'<# I> © ©q io 

©q ;oo^HaocowrHowooipi>oco>p^o © ^ ©q ; h 

05 ^I^CD-^lO»OOvbt : 'CDiO>CicbTH^-ilo4lOiOO-<chrH * h 

r— 1 


124-25 


207-63 


•5485 


Pithecan- 

thropus. 


CO t" LO oqcD t> O H©N>fl CO © 00 © 

CO ©q CO 00 0505 cpcpo-f loooiocq 

MHHOOO^OCDMOCOCoilHOOOOTtlcbcbMOOO 


51-92 


220-99 


•2349 


Anthropoid. 


lOO lo oo lO -«cH . 00 CO 00 loco 

i—i io 05 i—i cpcp.ocooo ; r^co; 

ooo^noooooorboooosb © © © © © h © 


10-66 


206-79 


•0515 


Maximum. 


I (NDHOt^t'00OHCD'^(NDC0t'O'^l0l>00©>i(»0O© 
©t-^©orHHffl©coxcqoco^^co^ipHicioiot^co© 
-^^i-Hcb-^rH05cbi^-id5iAd5d5Gbd'Gbi0GbcDiAiocbi0'-HG-^ 

I—i 1 — 1 1 — 1 I—I I—I I—I I—I 


220-99 








05cqoq©qo5'^05CDoor-HrH©qTtiiocoo5iO'^TjHcDioiocoo5ioo5 
^OHHt'Ht'HOOOHOOCO'^l>ffii<THt'<MXDrtOO®cO 
t-coio<McocorH©qior-r-co©qoo-itfi05©©05ioiOTtHc©iOTlHio 
©©©©©©©©00 00 00 00 001>t^©t^Ir^iOi©Tt<'^'^i— i©io 


Total . 


Pos. ) 
Max. / 


3 ® 

Ph Pm 


No. 


i— ioqco-^iocDt^oo©©i— icqco-^io©r^oo©©rHcqcoTt<t^ro 
hi— ii— ii— iHHHHr— i^noqcqoqcqoqcq 1 ^ 



160 



Proceedings of the Royal Society of Edinburgh. [Sess. 



Table A. — Comparison of the Nasio-Inion Length. 





Minimum. 


Average. 


Maximum. 


1. Four Kalmucks ..... 


154 


162*5 


169 


2. Twenty Europeans, unsexed 


154 


168 


178 


3. Pithecanthropus erectus .... 


. . 


168 




4. Forty-four Tasmanians, unsexed 


144 


169*7 


183 


5. One hundred Australians, unsexed . 


157 


173*8 


191 


6. Gibraltar 




182*1 




7. Cro-Magnon old man .... 




194*2 




8. Three Spy-Neandertal .... 


192 


196*3 


199 



Anthropoids, Briix, Galley Hill, Veddahs, Dschagga negroes, Egisheim, Briinn, 

and Stangenas absent. 



Table B. — Comparison of the Glabella-Lambda Length. 





Minimum. 


Average. 


Maximum. 


1. Pithecanthropus erectus . 




171 




2. Forty-eight Tasmanians, unsexed . 


162 


173*2 


189 


3. Gibraltar ...... 




177 




4. One hundred Australians, unsexed . 


161 


178*6 


194 


5. Egisheim ...... 




185 




6. Briix (Schwalbe) ..... 




185 




7. Three Spy-Neandertal (Klaatsch) . 


185 


185*3 


186 


8. Cro-Magnon old man (Klaatsch) 




193 




9. Galley Hill 




194 




10. Briinn ....... 




197 





Anthropoids, Gibraltar, Kalmucks, Veddahs, Europeans, and 
Dschagga negroes absent. 



Table C. — Comparison of the Lambda-Glabella-Inion Angle. 





Minimum. 


Average. 


Maximum. 


1. Pithecanthropus erectus (Klaatsch) . 




10 




2. Three Spy-Neandertal (Schwalbe) . 


15 


15*8 


16*5 


3. Galley Hill (Klaatsch) .... 




17 




4. Briinn (Klaatsch) ..... 




17 




5. One hundred and sixty-eight Australians 








(Berry, Robertson, and Klaatsch), 








unsexed . . 


13*5 


17*1 


22*5 


6. Cro-Magnon old man (Klaatsch) 




17*5 




7. Fifty- three Tasmanians (Berry, Robertson 








and Klaatsch), unsexed 


15 


18 


23 


8. Briix (Schwalbe’s estimation) 




20 




9. Forty-three ancient Egyptians (Schwalbe) 


15 


20*7 


29 


10. Twenty-five Dschagga negroes (Schwalbe) 


17 


21*5 


28 


11. Thirty-five Europeans (Schwalbe) . 


17*5 


22 


30 


12. Gibraltar (Sollas) . . . . 




24? 





Anthropoids, Kalmucks, Veddahs, Egisheim, and Stangenas absent. 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 161 



Table D. — Comparison of the Distance of the Bregma Foot-Point from 
the Glabella on the Glabella- Lambda Line. 



1 


Minimum. 


Average. 


Maximum. 


1. Pithecanthropus erectus (Klaatsch) 




79-5 




2. Gibraltar ...... 




82-2? 




3. Forty-eight Tasmanians, unsexed 


65 


82-3 


96 


4. One hundred Australians, unsexed . 


73 


85-3 


101 


5. Galley Hill (Klaatsch) .... 




91-5 




6. Cro-Magnon old man (Klaatsch) 




91-5 




7. Briinn (Klatsch) 




92-7 




8. Three Spy-Neandertal (Klaatsch) 




98 




9. Briix (Schwalbe estimated) 




100-5 





Anthropoids, Kalmucks, Veddahs, Europeans, Dschagga negroes, Egisheim, 
and Stangenas absent. 



Table E. — Comparison of the Bregma Foot-Point Glabella-Lambda Index. 





Minimum. 


Average. 


Maximum. 


1. Pithecanthropus erectus .... 




46-4 




2. Gibraltar ..... 




46-4? 




3. Forty-eight Tasmanians, unsexed 


40-1 


46-7 


51-8 


4. Briinn ....... 




47 




5. Galley Hill 




47-1 




6. One hundred Australians, unsexed . 


40-9 


47-2 


53-1 


7. Cro-Magnon old man . 




47-4 




8. Three Spy-Neandertal .... 




52-8 




9. Briix 




54-3 





Anthropoids, Kalmucks, Veddahs, Europeans, Dschagga negroes, Egisheim, 

and Stangenas absent. 



In the foregoing tables there are several points to which we should like 
to direct particular attention. 

Firstly, as regards the tables, Nos. I. to XXVII. are those already 
employed in our previous Tasmanian work (3). Tables A to E inclusive 
comprise the additional observations which we then stated we intended to 
employ in our Australian researches, and which are, therefore, now included. 
It is a matter of congratulation that we are enabled to incorporate the five 
additional observations not previously made upon the Tasmanian. Mr L. 
W. G. Buchner, a recently appointed Victorian Government Research 
Scholar in the Physical Anthropological Laboratory of the University of 

Melbourne, has been engaged in an examination of the Tasmanian facial 
VOL. xxxiv. 11 



162 Proceedings of the Royal Society of Edinburgh. [Sess. 

skeleton, and has kindly furnished us with the necessary Tasmanian data 
under Tables A to E inclusive for comparison with the Australian. 

Secondly, as regards the numerical order of the Tables. In our previous 
Tasmanian work, Tables I. to XXVII. were simply set forth in the accidental 
order in which the observations were recorded. Our fellow-worker, Dr 
K. Stuart Cross, subsequently showed (4) that these morphological observa- 
tions were not all of equal morphological value. He set them forth in their 
correct order of value, and in this vrork we have arranged Tables I. to 
XXVII. in Dr Cross’s order. Table II. of the Tasmanian work becomes 
therefore now Table I., Table XVII. similarly becomes Table II., and so on 
as determined by Dr Cross. Tables A to E still retain their accidental 
order of observation. 

Thirdly, as already stated, additional objects of comparison have been 
incorporated in the present tables whenever it was possible to secure 
accurate data. It is, however, a matter for regret that so few figures 
dealing with the morphological form analysis of the human skull on the 
lines advocated by Schwalbe and Klaatsch are as yet available, and hence, 
although extended, the present tables are not even yet as complete as we 
should have desired. If our colleagues in Europe would undertake the 
necessary researches on British long and round barrow skulls, on modern 
Europeans, on pre-historic and modern Egyptians, and so forth, the problem 
of the true place in Nature of the Australian and Tasmanian aboriginal 
inhabitants would be rendered simpler. These difficulties notwithstanding, 
a comparison of our previously published Tasmanian tables with those now 
incorporated will show that the latter have been increased. Thus the 
Egisheim and Stangenas primitive crania have been included (Frederic, 8) 
whenever the necessary figures were available. The 17 Maories first 
mentioned in Table VII. are from the work of Mollison (9). The 
Andamanese Islanders and the 90 Italians incorporated in Table XXI. are 
from the Royal College of Surgeons Catalogue of Osteology, and have been 
worked out therefrom by ourselves. The 176 Europeans (Scotch) mentioned 
in the same table are from the work of Sir William Turner (10). 

The Relative Evolutionary Positions of the Australian and 

the Tasmanian. 

In our previous Tasmanian communication we stated that we thought 
the Australian would stand on the plus side of the Tasmanian — that is to 
say, we confidently expected to find that the Australian would be a more 
highly evolved morphological type than the Tasmanian. This expectation 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 163 

has not, however, been realised. Mr W. M. Holmes, of the Natural 
Philosophy Department of this University, has been good enough to apply 
Cross’s mathematical formula to the results of the observations recorded in 
the several tables. He finds the Australians are represented by the figure 
0*739, and the Tasmanians by 0*779. The complete results are graphically 
represented in fig. 2, and numerically in Table XXIX. An examination 
of fig. 2 will demonstrate that the Australian, as regards his skull type, is 
less highly evolved, morphologically, than is the Tasmanian. How far this 
result agrees with one’s preconceived conceptions, it is difficult to say ; but 
probably an extract from Nature of th$ 14th July 1910, taken from a 
review of Professor Keith’s Hunterian Lectures on the Anatomy and 
Relationships of the Negro and Negroid Races , best reconciles the position. 
It is there stated that “ an analysis of the cranial features of the aborigines 
of Tasmania and of Australia shows that we have in these two races an 
early stage in the differentiation of the negro and negroid races of mankind. 
The Tasmanian is the most primitive type of negro yet discovered; the 
Australian, on the other hand, although deeply pigmented and less Simian 
in some features than the Palaeolithic European, is the most primitive 
representative of the negroid race. Negroid as he is, the native Australian 
represents a stage in the evolution of the dominant non-negroids of the 
northern hemisphere. It is a remarkable fact that the negro and negroid 
races occur side by side, not only in Australasia, but in Asia proper and 
in Africa.” 

If this be the case, our results would appear to harmonise with the 
views expressed in the above quotation, for our work simply shows that, as 
regards his cranium at all events, the negroid Australian has not progressed 
quite so far in the evolutionary scale as has the Tasmanian negro. 

Are the Australians and the Tasmanians One and the 

Same Pace ? 

If we have interpreted the above extract from Nature correctly, it 
would appear to be the opinion of the reviewer that the Australians and 
the Tasmanians are, in effect, different types, if not, indeed, different races. 
Sir William Turner, too, would appear to hold the same view, for, in 
his “ The Craniology, Racial Affinities, and Descent of the Aborigines of 
Tasmania” (11), he states : “From the consideration of these characters the 
skulls support the opinion, based on the study by so many observers of 
the external features, that the existing aborigines of Australia are distinct 
from the Tasmanians, although the presence, in a proportion of the natives 



164 Proceedings of the Royal Society of Edinburgh. [Sess, 




prehistoric and recent forms of man. 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 165 

of South and West Australia, of skulls in which the height was less than 
the breadth, the not infrequent sunk sagittal suture, the more marked 
parietal eminences, and the antero-posterior parietal depressions, point to a 
possible amount of intermixture and racial affinity of these Australian 
tribes with the Tasmanians.” 

The Breslau school of anthropologists apparently hold the directly 
opposite view, for Basedow (12), a pupil of Professor Klaatsch, states that 
“ the few superficial characteristics of the Tasmanian skull are not sufficient 
proof of his different origin from the Australian. It appears much more 
probable that in consequence of the comparatively recent separation of 
Tasmania from the mainland the Tasmanians have from that time first 
inherited their superficial differential characteristics.” Basedow concludes 
by stating quite bluntly that the “ Tasmanian was an insular form of the 
genuine Australian.” The pupil’s view is apparently held by the master, 
for we find Klaatsch stating that “ the Tasmanians do not show any nearer 
relationships to other races than the Australians.” He adds that the 
separation of the two races probably occurred a very long time ago 
Alsberg (13) would appear to agree with Klaatsch. 

Between the two extreme views above quoted there appears to be an 
intermediate opinion represented by Haddon, Keane, and many other 
anthropologists. For the illustration of this school of thought one char- 
acteristic quotation must suffice, though it would be easy to multiply 
examples. Haddon (14), in his Races of Man and their Distribution , 
published in 1911, says: “It is generally believed that Australia was 
originally inhabited, or at all events in parts, by Papuans or Negritoes, 
who wandered on foot to the extreme south of that continent. When 
Bass’ Strait was formed, those who were cut off from the mainland formed 
the ancestors of the Tasmanians, who never advanced beyond an early 
stage of Stone-Age culture. Later, a pre-Dravidian race migrated into 
Australia, and overran the continent and absorbed the sparse aboriginal 
population. Since then they have practically remained isolated from the 
rest of the world. Their languages bear no relation to the Austronesian or 
Oceanic linguistic family.” A somewhat similar view was advanced by 
one of us in 1909 (Berry, 6). 

Whether the divergent views as to the commonality of race of 
Australians and Tasmanians be quoted in extenso or but briefly as above, it is 
clear that all are based on either pure theory or on certain slight superficial 
osteological resemblances or differences according to the opinions of 
the author. 

We now propose to submit this question of the community of race or other- 



166 



Proceedings of the Royal Society of Edinburgh. [Sess. 

wise of the Australian and Tasmanian to a somewhat severe proof. Whatever 
may be the result, it must be remembered that it is the first time that such 
an attempt has been made on the lines of strictly severe scientific analysis ; 
and further, that in submitting the question to such proof, we are now 
enabled to deal with the largest numbers of Australian and Tasmanian 
crania which have ever yet been employed ; and lastly, that the application 
of such an analysis to what previously has been mere theory is due to the 
introduction of some ingenious craniological methods by Dr Th. Mollison, 
formerly of Zurich, and now of Dresden. 

In 1908 Mollison published in the Zeitschrift fur Morphologie und 
Anthropologie his “ Beitrag zur Kraniologie und Osteologie der Maori ” (9). 
In this paper he introduced for the first time what he then termed the 
“ Abweichungsindex.” The object of what in English we should term the 
“ variation index ” is to discover if two skulls belong to one and the same 
race or not, and the procedure adopted is as follows : — 

Multiply the distance of the individual from the average value of the 
standard type group by 100, and divide the product by the sum of the 
extremest distance of the group on the minimum or maximum side of the 
variation breadth. Thus a standard group of skulls (see fig. 3) has an 
average greatest breadth value of 135, and a cephalic index average value 
of 76. Another skull to be compared with this group has a greatest 
breadth of 126 and a cephalic index of 64. The question to be answered 
by the variation index is, Does this skull belong to the same race as the 
standard group or not ? The distance of the doubtful skull from the 
average value of the standard group is for the greatest breadth 9, and for 
the cephalic index 12. Multiply these figures, both of which are on the 
minimum range of variation side of the standard group, by 100, and divide 
by the greatest range of variation of the standard group on the maximum 
or minimum side as the case may be : in this case the minimum side. The 
correct figures will therefore be found in the example quoted by subtract- 
ing for the greatest breadth 129 from 135, and for the cephalic index 70 
from 7 6. In each instance the difference is 6. If this calculation be worked 
out in the manner indicated, it will be found that the variation index for 
the imaginary object to be compared with the standard group is, for the 
greatest breadth 150, and for the cephalic index 200. 

To compare the variation indices of a large number of characteristics, 
draw a straight line which shall be supposed to pass through the average 
figures of each characteristic. Parallel to this draw two lines at arbitrary 
distances and supposed to represent the minimum and maximum range of 
variation of each observation from the average for the same; in each 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 167 

instance the distance of the minimum or maximum parallel from the line 
of average measurement is supposed to represent 100 per cent. 

The variation index for the object to be compared is now set at its 
correct distance from the average line on the plus or minus side. Connect 
these several points together, and a graph is at once constructed which, if 



Greatest 

Breadth. 



Maximum Range of Variation— 141 



Average Value 



—135 



Minimum Range of Variation.— 129 



Cephalic 

Index. 



83 



76 



70 




0 



100 %. 



Skull to be compared with 

TYPE GROUP. 





1. Subtract 126 from 135 = 

1. Subtract 129 from 135 = 

2. Subtract 64 from 76 = 
2. Subtract 70 from 76 = 



9 x 100 
6 

12 x 100 
6 



150. 



200 . 



Fig. 3. — To illustrate Mollison’s Yariation Index. 



it lies within the parallels, is proof that the compared stock is of the same 
race as the original group. If it be outside, then the compared object and 
the original group are not of the same species. A glance at the figure 
referred to (fig. 3) will illustrate the whole method of working Mollison’s 
variation index, and will also demonstrate the fact that the suppositious 
skull to be compared with the crania of the standard group or type is of a 
different race. Mollison’s original paper contains some highly instructive 
examples of the working of this index. Amongst other things he was 



168 



Proceedings of the Royal Society of Edinburgh. [Sess. 

enabled to prove that a skull in the Zurich collection alleged to be that of 
a Maori was not a Maori skull, but that of an Australian aboriginal. 

It must not be supposed that in adopting Mollison’s method we are 
breaking new ground. His method has already been adopted by Czeka- 
nowski (15) for the solution of a problem almost precisely similar to that 
with which we are confronted — namely, the racial affinities of the Central 
African pigmies ; by Oppenheim, in his “ Zur Typologie des Primaten- 
craniums ” (16) ; and by Radlauer (17) ; and we believe that we are correct 
in stating that all these authors have accepted the correctness of Mollison’s 
methods and have abided by the conclusions to which that method led them. 

In fig. 4 the Tasmanian is taken as the basis. The 32 morphological 
observations made by us upon the cranium are indicated by the numbers 
1 to 27, and the letters A to E, inclusive. The centre line in that figure 
labelled “ Tasmanian average ” is supposed to represent the average values 
for these 32 observational counts on the Tasmanian cranium. At an 
arbitrary distance from this centre line are drawn two parallel lines which 
indicate the maximum and minimum ranges of variation of the Tasmanian 
from the average, and which are uniformly treated throughout as being 
equal to 100 per cent. The Australian “ variation index ” is plotted in for 
each of the 32 counts of the investigation, and is indicated in the figure by 
the dotted line. It will be clearly evident that the Australian “ variation 
index” falls altogether within the Tasmanian maximum and minimum 
ranges of variation, thus proving conclusively, according to Mollison, that 
Australian and Tasmanian are one and the same race. 

Mollison, in the paper already referred to, speaking of his variation 
index, says, “ Schon fur die Yergleichung in einem einzelnen Merkmal ist 
dieses Verfahren zweckmassig. Sien voller Wert zeigt sich aber erst dann, 
wenn wir eine grossere Reihe von Merkmalen vor uns haben, bezuglich 
deren wir die Stellung des Individiums zu der Grupp beurteilen sollen.” 

As Mollison is clearly of opinion that his method will always furnish 
more accurate results if the procedure be made to include as large a number 
of observations as possible, we have thought it desirable to supplement 
these 32 morphological observations of the form analysis of the skull by an 
additional series of craniological observations specially recorded by us on 
both Australian and Tasmanian for this special purpose and which have 
little or nothing to do with the form analysis of the skull. 

These additional observations are 14 in number as given on page 146, 
and have been specially selected by us for two reasons : firstly, because 
they have nothing to do with the measurements and angles concerned in 
our investigation of the form analysis of the skull ; and secondly, because 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 169 




\ 



170 Proceedings of the Royal Society of Edinburgh. [Sess. 

they are those uniformly recorded in the Osteological Catalogue of the 
Royal College of Surgeons of England, and have, therefore, enabled us to 
make use of any further comparative data which we desired — an oppor- 
tunity of which, as will be seen later, we have availed ourselves. 

It will be noticed that one measurement, and one only, is common to 
the 32 form analysis counts and the 14 general craniological observations, 
and that is the maximum breadth. We have, however, availed ourselves 
of an increased number of Tasmanian skulls under this count from one of 
our previous communications, and this fact explains the slight divergence 
in the results obtained. 

The total number of observations now available — namely, 46, composed 




Fig. 5. — The Tasmanian Variation Index for 14 craniological observations 
plotted out upon the Australian as the basis. 

of the 32 form analysis counts and the 14 craniological observations — is the 
largest number which has yet been employed for the working out of 
Mollison’s variation index. Mollison himself only employed some 24 
observations, Czekanowski about 28, Oppenheim 8, and Radlauer 20. 

In fig. 5 these 14 general craniological observations are set out with 
the Australian as the base. The Tasmanian variation index is plotted 
out in a dotted line, and the results conform in every respect to those 
already obtained by the 32 form analysis figures. In all cases the varia- 
tion index falls altogether within the maximum and minimum range of 
variation, thus again proving conclusively, according to Mollison’s method* 
that Australian and Tasmanian are one and the same race. 




1913-14.] The Place in Nature of the Tasmanian Aboriginal. 171 



The Physical Relations of the Australian and Tasmanian to 
the Spy-Neandertal Race. 

It has repeatedly been stated that the Australian aboriginal is, in his 
physical construction, so closely related to the Spy-Neandertal men as to 
justify the assumption that they are of the same race, or at all events have 
been derived from the same stock. Thus Klaatsch (18) says, “ The general 
formation of the skull capsule and the form of the facial skeleton have 
led him to the conclusion that the Australian and the Neandertal race 
have many features in common as heirlooms from a common primitive 
stock from which the Australian and the Neandertal race have developed 
in different directions.” 

von Luschan (19) probably shares this belief, for he says, “The primi- 
tive qualities or characters (Eigenschaften) of the Australian show a con- 
siderable amount of similarity with similar characteristics of the oldest 
European man, which possibly underlies a real relationship.” 

Stratz (20), in advancing his ideas for the correct racial divisions of 
mankind, says that amongst the “ protomorphic ” races he regards the 
modern Australian as amongst those which stand nearest to the oldest 
monogenetic common primitive stock. 

Schoetensack (21), in advancing his theory that man originated in 
Australia, states that in Pliocene times the fauna of Australia contained 
not even one single dangerous rival for the evolution of man. Many 
human varieties could have developed themselves under these conditions, 
and the modern Australian is even to-day extraordinarily rich in varieties ; 
the closely allied form relations of the oldest European human species 
(Spy-Neandertal) turns one’s thoughts towards the emigration of such a 
variety. 

Alsberg (13) agrees with Klaatsch as to the primitive nature of the 
Australian and points to the Neandertal species as a step in the ancestral 
series. 

In view of the above opinions — and they could be multiplied — we thought 
that it would be of some interest to apply Mollison’s variation index to the 
alleged relationship of Australian and Spy-Neandertal. For this purpose 
we have employed the 32 form analysis observations only, as it is obvious 
that the 14 general craniological characteristics, including as they do 
orbital and nasal measurements and indices, are not available for the Spy- 
Neandertal group. 

In fig. 6 the variation index of the three Spy-Neandertal crania is 
plotted out upon our 100 Australians as a basis. A glance at the resulting 



172 Proceedings of the Royal Society of Edinburgh. [Sess. 





1913-14.] The Place in Nature of the Tasmanian Aboriginal. 173 

graph will show that here a totally different result is produced than in the 
similar graphs for Tasmanians and Australians. If Mollison’s index be a 
correct guide to this question of similarity of race, it is clear that here we 
are dealing with two entirely different races. The Spy-Neandertal varia- 
tion index graph is seen to be highly irregular, and is by no means confined 
within the maximum and minimum range of Australian variation. 

This fact is still more strikingly brought out in fig. 7, where the 
Tasmanian is taken as the basis, and on it are plotted out the variation 
indices for the Australian and the Spy-Neandertal group. The variation 
index for the Australian is seen to be very uniform and to fall altogether 
within the Tasmanian range of variation, whilst that for the Spy-Nean- 
dertal group is most irregular and is altogether outside the range of varia- 
tion more often than within it. This figure conclusively demonstrates one 
or other of two things : either that Mollison’s variation index is not a 
reliable guide to the differentiation of race, or that the views quoted as to 
the unity of type of Australian and Spy-Neandertal are erroneous. It 
must, we think, be admitted by any fair-minded critic that one or other 
of the two things must therefore, in future, be eliminated from scientific 
discussion. 

A closer glance at the variation index for the Spy-Neandertal race on 
either the Australian or the Tasmanian (figs. 6 and 7) will show that, 
notwithstanding the marked irregularity of the graph, the index occa- 
sionally falls within the range of variation. In the case of both the 
Australian and the Tasmanian this happens 13 times out of 32. If 
Mollison’s variation index be, indeed, any reliable guide to this question 
of differentiation of race, then the most we can admit for the alleged 
relationship of Australian to Spy-Neandertal is that they have something 
in common, but that that something is so little that the view of commonality 
of race between the two must be abandoned. We agree therefore with 
Schwalbe (22), w T ho says, “ The Australians are certainly a primitive race, 
but have nothing whatever to do with Homo primigenius” 

The Relationship of Australian and Tasmanian to a Supposed 
Pure Race like the Andamanese. 

The next use which we propose to make of Mollison’s variation index 
is to test the relationship, if any, of the Tasmanian and Australian 
with a supposed homogeneous race like the Andamanese Islanders. This 
will be a useful comparison, because it has been thought by some observers 
that the Australians are very closely akin to these Islanders. Quite apart 



174 



Proceedings of the Koyal Society of Edinburgh. [Sess. 




Fig. 7. — The Australian Variation Index and the Spy-Neandertal Variation Index plotted out upon the Tasmanian as the basis. 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 175 

from this the comparison will be of interest, inasmuch as certainly both 
Tasmanians and Andamanese have long been isolated from contact with 
other races. 

For the purposes of this comparison we have been compelled to make 
use of the 14 general craniological observations only, the reason being 
that we have had no means of access to the necessary figures for the form 
analysis of the Andaman Islanders skull. In fact we do not believe such 
figures exist. The data that we have been able to employ are derived from 
the Osteological Catalogue of the Royal College of Surgeons of England. 
They comprise 19 skulls of Andamanese upon which we have utilised the 
necessary figures for the 14 general craniological observations. 

In fig. 8 the Andamanese Islander is utilised as the base. Upon this 
are plotted out the variation indices for both Australian and Tasmanian. 
The resulting graphs are again highly irregular and, according to Mollison, 
are sufficient proof that the Australian-Tasmanian race is something dif- 
ferent from the Andamanese Islander. A closer inspection of the graphs 
will, however, show that the Australian-Tasmanian variation indices fall 
within the Andamanese range of variation 7 times out of 14 — that is, in 
50 per cent. If this index of Mollison tells us anything at all, it is that, 
notwithstanding the difference in race, the Australian-Tasmanian race 
is more nearly related to the Adamanese Islander than to the Spy- 
Neandertal group. 

The Relationship of Australian and Tasmanian to a Heterogeneous 
Race like the Modern Italian. 

The last use which we propose to make of Mollison’s variation index 
is to test the racial relationships of the Australian and Tasmanian with an 
admittedly heterogeneous race like the modern Italian. We have selected 
the modern Italian for this comparison for three reasons : firstly, because 
the modern Italian is admittedly and undoubtedly a mixed or impure race ; 
secondly, because modern Italians and the indigenous inhabitants of 
Australia and Tasmania cannot possibly have any racial relationships in 
common ; and thirdly, because the Catalogue of the Royal College of 
Surgeons of England enabled us to command a sufficiently large number 
of Italian data, namely 90, to eliminate the possibility of error due to 
the use of insufficient numbers. 

In this comparison we have again been restricted to the 14 general 
craniological observations, and for the same reasons as in the case of the 
Andamanese Islanders. 



176 



Proceedings of the Royal Society of Edinburgh. [Sess. 




1913-14.1 The Place in Nature of the Tasmanian Aboriginal. 177 

o 

In fig. 9 the modern Italian is utilised as the base, and upon it is plotted 
out the Australian variation index. As the latter falls within the extreme 
ranges of variation of the former, the graph would lead us to believe, if 
Mollison’s index be indeed a reliable guide to racial affinities, that the 
Australian aboriginal and the modern Italian are one and the same race — 
a conclusion which, we take it, will not be credited by any anthropologist, 
certainly not by ourselves. 

It may well be, that, in view of this extraordinary result, some anthro- 
pologists will be inclined to discredit Mollison’s index altogether and refuse 
to accept it as a means of distinguishing diverse racial types. On the 
other hand, there are the undoubted facts that in the hands of Mollison 




Fig. 9. — The Australian Variation Index for 14 craniological observations plotted 
out upon the Modern Italian as the basis. 



himself, and in the work of Czekanowski, Oppenheim, Radlauer, and our- 
selves it has given results which confirm the conclusions attained from other 
sources and which would lead to the supposition that it is a fairly accurate 
method of eliminating racial types one from the other; but the Italian- 
Australian-Tasmanian comparison just instituted seems to prove conclusively 
that the index is not an infallible guide and that its findings must be 
regarded with a considerable amount of caution. For ourselves, for 
reasons to be presently adduced, we have been led to the conclusion that 
Mollison’s variation index is only a reliable guide to racial difference 
provided the range of variation of one, at least, of the racial types compared 
is but small. It is perfectly obvious to anyone who has worked with the 
index that as the range of variation increases it gradually encroaches on 

the variation index and eventually necessitates the latter falling within 
VOL. xxxiv. 12 



178 Proceedings of the Royal Society of Edinburgh. [Sess. 

the former and thus gives rise to the reductio ad absurdum results of our 
modern Italians, Australians, and Tasmanians. 

The Range of Variation. 

We now propose to consider the very important question of the range 
of variation in the Australian, Tasmanian, and the other homogeneous and 
heterogeneous races selected by us for comparison, in order to see what light 
such a study throws on the vexed question of the purity of origin or 
otherwise of the Australian aboriginal. 

Almost every author who has investigated Australian osteology has 
been impressed with the great range of variability displayed by his results. 
Thus Klaatsch (23) says that the study of the variability of the Australian 
is of the greatest significance. Wetzel (24), from his researches as to the 
amount of variation in the vertebral column of the Australian, came to the 
conclusion that the total amount of variation in the osseous vertebrate 
column of the Australian is considerably greater than in the European, but 
that, on the other hand, the variation in individual sections is less in the 
Australian than in the European, and that females are the least variable. 
Stratz (20), in advancing his theory of the racial division of mankind, states 
that the protomorphic races — especially the Australians — are characterised 
by great individual variability. Schoetensack (21) also states that the 
modern Australian is even to-day extraordinarily rich in varieties. It is 
unnecessary to multiply examples of the current belief that the Australian 
is extraordinarily rich in his range of variation, because, as will now be 
shown, our investigations confirm this view. 

Of the Tasmanian there are necessarily fewer opinions, for the sufficient 
reason that he was extinct before it was realised how important this study 
of the range of variability is. In discussing, therefore, the range of varia- 
tion exhibited by the Tasmanian we are practically breaking new ground, 
apart, of course, from the generally accepted belief that as a homogeneous 
race the Tasmanian would tend to display a less extended range of varia- 
tion than in undoubted heterogeneous races. 

Comparison of the Range of Variation in Supposed Pure Races 
like the Andamanese and Tasmanians with an Admitted 
Heterogeneous Race like the Modern Italian, with the object 
of Establishing the Place of the Doubtful Australian. 

In order to appraise the amount of variation in the pure, mixed, and 
doubtful races selected for the comparison now to be established, we have 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 179 

selected the Tasmanian as the basis. In fig. 10 the maximum and minimum 
range of variation of this race is represented by two horizontal lines which 
are supposed to pass through the extremes of variation uniformly regarded 
as being equal to 100 per cent. If, for example, the average maximum 
breadth of a series of Tasmanian skulls be found to be 135 with a minimum 
breadth of 120, the range of variation on the minimum side would be 15. 
If now the average maximum breadth of a series of Australian crania be 

o 

found to be 131 with a minimum of 120, the range of variation would be 
11 and the relative values of the Tasmanian and Australian ranges of 
variation would be expressed by the formula as 15 (Tasmanian) is to 100 
so is 11 (Australian) to the answer, namely 73 in round numbers. As the 
data from which our fig. 10 is compiled include other skulls besides those 
specifically dealt with here and taken as stated from the Royal College of 
Surgeons Catalogue, we can only indicate generally the process by which 
the results are attained. We may, however, add that the very greatest 
care has been taken in the calculations, which have been made throughout 
by mechanical appliances. 

The most cursory glance at the graph shows that the range of variation 
is in the Australian greater than in the Tasmanian. It further shows 
that certain individual Australians are at a much lower position in the 
evolutionary scale than are the most lowly of the Tasmanians ; that certain 
individual Australians have, on the other hand, attained a higher position 
than have the most highly evolved Tasmanians ; whilst lastly, the applica- 
tion of Cross’s formula demonstrates that the average Australian remains 
at a slightly lower level in the evolutionary scale than does the average 
Tasmanian. 

Concerning the Andamanese the same graph, fig. 10, demonstrates 
that, as judged by the range of variation, the Andamanese are an even 
purer race than are the Tasmanians, but that, with one or two exceptions, 
the most advanced Andamanese has not attained so high a position in the 
evolutionary scale as have either the Tasmanian or the Australian. 

Regarding the primary object of the graph, it will be evident that the 
Australian, in his maximum and minimum ranges of variation, is more 
closely related to the admittedly mixed race — the Italian — than to the two 
supposed pure races. To test the point still further, we have submitted the 
range of variation in all the compared races to a numerical proof. The 
race taken as the basis, the Tasmanian, is regarded as possessing an amount 
of variation equal to 100 per cent. The variations of the other races are 
calculated therefrom in percentages, added together and divided by the 
number of observations — 14. As both the maximum and minimum series 



180 



Proceedings of the Royal Society of Edinburgh. [Sess. 




Australian 



Modern Italian 



TAfMMlAN (SAX^UM 
10M 



Andamanese 



TA&MANiAJN MINIMUM 



RANGE OF VARIATION 



ZBqL 



Fig. 10. — The Ranges of Variation of the Australian, Modern Italian, and Andamanese for 14 
general craniological observations plotted out upon the Tasmanian as the basis, and expressed 
in percentages of the latter. 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 181 



have to be taken into consideration, the divisor is naturally twice 14. The 
results are as follows : — 



Supposed homogeneous races — 
Andamanese . 
Tasmanians 

Admitted heterogeneous race — 
Modern Italians 
Race of doubtful origin — 
Australians 



62*7 per cent. 
1000 „ 

130 per cent. 

141*9 per cent. 



Summary of the Observed Facts. 

In view of the complicity of the problem now under consideration, it 
would seem advisable here to recapitulate the new facts brought out in the 
present paper before we pass to their interpretation. 

1. The present work contains the detailed measurements of 32 form 
analysis measurements of 100 Australian aboriginal crania not previously 
examined. The measurements so recorded are those introduced by Schwalbe 
and Klaatsch, and have been previously utilised by us for some 52 Tasmanian 
crania. 

2. The present work also incorporates, but does not give the detailed 
measurements of, 14 observations of a general craniological character, but 
more particularly on the face, of the above-mentioned 100 Australian and 
52 Tasmanian crania. 

3. For purposes of comparison the corresponding series of measurements, 
wherever available, have been worked out from other sources for 3 Spy- 
Neandertal crania, 19 Andamanese Islanders, and 90 modern Italians. 

4. The data resulting have been utilised in order to see what evidence 
they afford as to the purity of stock or otherwise of the Australian ; hence 
the races selected for comparison have been specially chosen as representa- 
tives of either admittedly pure races or of equally undoubted impure races. 

5. The use of Mollison’s variation index shows that Tasmanians and 
Australians are a common stock, and that both these races are very much 
more closely related to each other than they are to either Spy-Neandertal 
or Andamanese. 

6. Mollison’s index is shown to be an unreliable guide to the differentia- 
tion of race once the range of variation in one or both of the compared 
stocks exceeds a certain limit. What this limit is requires further proof, 
but is certainly exceeded by Australians and modern Italians. A study of 
the range of variation shows that the Australian agrees much more closely 



182 Proceedings of the Royal Society of Edinburgh. [Sess. 



with an admittedly impure race like the modern Italian than with supposed 
pure stocks like the Andamanese or the Tasmanians. 

7. A study of the mean values of all the observations recorded as shown 
by Cross’s method of dealing with such calculations proves that the average 
Australian is not such a highly evolved type as was the average Tasmanian. 

Interpretation of the Facts. 

Biasutti (25), in a recently published paper the original of which is not, 
unfortunately, available to us in Melbourne, has apparently devoted some 
attention to Tasmanian and Australian literature, and assumes therefrom 
that the Tasmanian is the older of the two types, was developed on the 
Australian mainland, and migrated thence to Tasmania. The Australian 
race has been developed from this primitive type and has preserved itself 
as a mixture, and by insular isolation. 

It is impossible for us, under the circumstances, to say whether Biasutti 
regards his theory as either new or original ; but it is hardly necessary to 
add that it is neither one nor the other, and we only notice the work at all 
for the simple reason that its author revives the opinion that the Australian 
aboriginal is a mixed type resulting from a cross, presumably with the 
older and more primitive Tasmanian type ; and this, be it noted, is the only 
theory which fits the facts adduced in this, and our other papers, as also 
certain other well-known ethnological, cultural, and linguistic data. 

Professor Sergi of Rome has recently published a most important mono- 
graph on the racial affinities of the Tasmanian and Australian, under the 
title “ Tasmanier und Australier ( Hesperanthropus tasmanianus spec.) ” 
(26). We consider ourselves indeed fortunate that the amount of detailed 
work in our present paper has so far delayed publication as to enable 
Professor Sergi to be first in the field, and this for reasons which will shortly 
be apparent. 

In this work Sergi has availed himself of the Tasmanian material 
recently made available by us in our “ Dioptrographic Tracings in Four 
Normae of Tasmanian Crania ” (5), as also of certain crania in Cambridge 
and elsewhere, and of the recent valuable contributions of Turner (11) and 
others. Of our own work Sergi states that he prefers to use the skull 
tracings delineated in the publication just referred to, because they are 
exact dioptrographic outlines in four normae of the skulls recorded, and 
adds that when a sufficient number of crania are so studied, their outlines 
can easily replace direct observation on the skulls themselves. 

From a study of these crania Sergi deduces the fact that they are 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 1 83 

lophocephalic, as are also many Australian crania. He states, therefore, 
that lophocephaly is an absolutely characteristic feature of a certain type of 
skull widely spread throughout the islands of the Pacific Ocean and which 
he recognises as the Tasmanian-Australian skull type. The geographical 
distribution of the lophocephalic Tasmanian-Australian skull is given by 
Sergi as extending from the Hawaii Islands in the north to New Zealand 
in the south, and from Australia in the west to Easter Island in the east, 
all inclusive. For the primeval home of this skull type Sergi, for reasons 
with which we are not especially concerned, but which seem sound, instances 
the American continent. For the primitive parent of this skull type he 
further proposes the name Homo tasmanianus, and adds that, whilst it is 
difficult to state exactly when he wandered into the Pacific Ocean from 
America, it is not improbable that the migration took place in late Pliocene 
or early Quaternary times and that he took with him no domestic animals 
of any kind. Homo tasmanianus wandered over the Australian continent 
into Tasmania, and, becoming isolated there, eventually developed into the 
Tasmanian aboriginal of recent times, and for him Sergi proposes the name 
Hesperanthropus tasmanianus spec. 

The many difficulties attending the Australian aboriginal are solved, 
says Sergi, by assuming that on the Australian continent there subsequently 
entered a Polynesian element, and in Sergi’s own words : “ die Kreuzung 
der Polynesier mit den urspriinglichen Australieneinwohnern tasmanischen 
Urspriings erzeugte eine Bastardvarietat, welche die heutigen Australier 
sind . . . die Australier hy bride Tasmanier waren.” For us this quotation 
is of such vital import that we may, perhaps, be pardoned for translating it 
as follows : — 

“ The crossing of the Polynesian with the original inhabitants of 
Australia of Tasmanian origin begot a bastard variety — the Australian 
aboriginal of to-day . . . the Australian aboriginal is a hybrid Tasmanian.” 

For the hybrid Australian Sergi proposes the name Hesperanthropus 
tasmanianus polynesianus, var. hybrida. 

The thesis here briefly set forth Sergi ably supports by many facts and 
different lines of evidence. With these lines of evidence we are not here 
specially concerned, nor are we vitally interested at the moment with the 
Polynesian character of the cross assumed by the distinguished Italian 
anthropologist. For ourselves we should have assumed an earlier cross 
than that emanating from the Polynesian element. This, however, is a 
minor point contrasted with the more important fact that Sergi, working 
by different methods and with additional material from other sources, comes 
to precisely the same results as ourselves — namely, commonality of origin 



184 Proceedings of the Royal Society of Edinburgh. [Sess. 

and race of Tasmanians and Australians with the latter subsequently 
resulting from a racial cross with the primitive stock. 

To Sergi’s theory, based, be it remembered, on facts which he has firmly 
established, let us now apply our own results. 

Commonality of origin of Australians and Tasmanians is shown in the 
present work by the results of Mollison’s variation index for Australian and 
Tasmanian. On no other grounds can the remarkably uniform results 
attained by us with this index be explained. Read in conjunction with 
Sergi’s study of lophocephaly we regard Homo tasmanianus as proved. 

That the Tasmanian aboriginal was as nearly as possible the pure 
descendant of Homo tasmanianus we regard as certain on account of (1) 
the results attained by Sergi himself; (2) the remarkably small range of 
variation found in the Tasmanian for the observations of the present work • 
(3) the equally small amount of variation recorded by Buchner (27) in his 
recent works on Tasmanian prognathism, craniotrigonometry, and curvature 
indices ; and (4) the close approach to unity for the coefficients of correlation 
already recorded by us in our biometrical study of the Tasmanian (2). It 
is thus clear that the morphological studies of Sergi, the craniological 
researches of Buchner and ourselves, and the biometrical work of Dr Cross 
and ourselves all alike testify to the purity of type of the Tasmanian and 
the truth of Sergi’s hypothesis. 

That the Australian aboriginal is a hybrid is, we believe, proved by (1) 
the results recently recorded by Sergi ; (2) the study in the range of 
variation adduced in the present work — a study which clearly proves that 
the Australian is more variable than an admittedly crossed race like the 
modern Italian ; (3) our own previously recorded study in the Australian 
coefficients of correlation ; and (4) Broca’s statement, quoted by Topinard 
(28), that it is only when the variations reach 15 or 18 per cent, that we 
can say with certainty that they are due to mixture of race. In the 
present work the Australian range of variation has been proved to be 
40 per cent, more than in the Tasmanian. 

If it be argued that we deduce too much from this range of variation — 
a study as yet largely in its infancy as regards the precise meaning to be 
attached to it — we reply in the words of Cossar Ewart, than whom there 
is no greater living authority on the subject of variation by crossing of 
types (29) : — 

“ Domestic animals reproduce themselves with great uniformity if kept 
apart ; but the moment one mixed up two different races, strains, or breeds, 
one did something that was difficult to put in words, but the result was 
what has been best described as an epidemic of variations.” 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 185 

Were we to interpolate in the above quotation the words “such as 
Homo tasmanianus and another primitive stock ” after the words “ strains 
or breeds,” and add at the end “ resulting in the Australian aboriginal,” it 
might stand as a perfect exposition of our views on the hybrid ity of the 
Australian. 

The hybrid character of the Australian is still further supported by 
Lapicque (30), Baudouin (30), and Kruger-Kelmar (31), and by such well- 
known ethnological facts as the use of the boomerang and throwing-stick 
in Australia and their absence in Tasmania ; the presence of a domesticated 
animal, the dingo, in Australia and its complete absence in Tasmania ; and 
the more evolved cultural character of the Australian flints as opposed to 
the more primitive Tasmanian type of instrument. The total absence of 
domesticated animals amongst the Tasmanians is further proof of their 
great antiquity. 

The study of language, too, indicates — some would say proves — the 
hybrid character of the Australian. No physical anthropologist would 
rely solely on linguistics as a proof of origin of race. Taken, however, 
in conjunction with somatology and ethnology, it is a valuable line of 
research. Mathew (32) has pretty well established the hybrid element 
in the Australian aboriginal, and here we find physical anthropology, 
range of variations, ethnology, and linguistics all alike pointing distinctly 
to the impurity of stock of the Australian. 

But what of the other side ? So far as our study of the literature 
enables us to judge, there are only some — to use his own word — 
“ superficial ” observations of Klaatsch, various unsupported theories of 
Schoetensack, Stratz, and others, the recent work of Basedow, and the 
difficulties — prior to the publication of this and the recently issued 
memoirs of Turner and Sergi — experienced by all in adequately explaining 
the position of the Australian. Basedow, it is true, boldly declared the 
Tasmanian to be but an insular type of Australian ; but as von Luschan 
(33) has dealt pretty trenchantly with this observer, we need not further 
consider him. There is nothing whatsoever in the environment, climate, 
animal or plant food of Australia and Tasmania, to account for the 
differences in types of Australians and Tasmanians, and for the enormous 
range of variation of the former. As regards the last-mentioned point, 
it is indeed rather the reverse. Dr Cherry, Professor of Agriculture in 
this University, assures us, as the results of his own observations and 
experiments, that the soil of the Australian continent is peculiarly deficient 
in phosphorus and that, relative to the soils of the European and other 
continents, those of Australia are in a miocene or pliocene condition. 



186 Proceedings of the Royal Society of Edinburgh. [Sess. 

Sofer (34), too, distinctly states that external influences do not affect 
races, whilst Doncaster (35) stresses heredity rather than environment. 
Here, then, is nothing to account for the excessive range of variation of 
the Australian as compared with the Tasmanian, and we are thrown back 
on the hypothesis already furnished — namely, hybridity, and the explana- 
tion of same as given by Ewart. 

From a study of the question in all its phases we are, therefore, forced 
to the conclusion that the Australian is a hybrid. 

One other interesting fact results from our study of the hybridity 
of the Australian aboriginal as deduced from his range of variation, and 
that is that the result of the cross has not benefited the race from the 
evolutionary standpoint. The modern-day Australian aboriginal stands 
rather nearer the anthropoid ape, or the common ancestor, than did the 
Tasmanian. Isolated individuals of the Australian race have, on the 
other hand, surpassed the Tasmanian. These facts are evidenced in the 
present work by the application of Cross’s formula to all the evolutionary 
objects under comparison and by the study of maximum and minimum 
ranges of variation for Australian and Tasmanian. 

Results. 

In conclusion we may say that, as a result of our prolonged study 
of Australian and Tasmanian craniology — a study which has now occupied 
us over five years and is still in progress, — we are led to the following 
conclusions : — 

1. The Australians and Tasmanians are the descendants of a common 
late Pliocene or early Quaternary stock which, for want of a better term, 
may be called with Sergi, Homo tasmanianus. H. tasmanianus had a 
wide range of distribution within the the islands of the Pacific Ocean 
(Sergi). 

2. The Tasmanian aboriginal was the almost unchanged offspring of 
this type, but evolved on his own lines and in his own way. 

3. The Australian aboriginal is the result of a cross between the 
primitive Homo tasmanianus and some other unknown race — Polynesian, 
according to Sergi; Dra vidian, according to Mathew — and is, therefore, 
a hybrid. From the evolutionary standpoint the result of the cross, 
whilst it has not been favourable to the race as a whole, has benefited 
individual members of it. Once evolved, the Australian has, like the 
Tasmanian, progressed on his own lines and in his own way. 

4. Both Australian and Tasmanian have attained, morphologically, 
to a higher stage in the evolutionary scale than is usually supposed. 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 187 

5. Neither Australian nor Tasmanian have any direct relationship 
with Homo primigenius as represented by the crania of the Spy- 
Neandertal men. The superficial points of cranial resemblance are 
explicable solely on the grounds of the remoteness of the ancestry. In 
the Spy-Neandertal crania we see them as they were ; in the modern 
Australian-Tasmanian type as they have evolved. 

6. The range of variability of structure is, in the Australian, as great 
as in any other known race of impure origin ; in the Tasmanian, on 
the other hand, it is as small as in any other known or supposed 
pure race. 

7. Mollison’s variation index as a test of type must be read in 
conjunction with the range of variation. 



LITERATURE. 

(1) Robertson, A. W. D., “ Craniological Observations on the Lengths, Breadths, 
and Heights of a Hundred Australian Aboriginal Crania,” Proc. Roy . Soc. Edin., 
vol. xxxi., 1910-11, pp. 1-16. 

(2) Berry, R. J. A., A. W. D. Robertson, and K. S. Cross, “ A Biometrical 
Study of the Relative Degree of Purity of Race of the Tasmanian, Australian, and 
Papuan,” Proc. Roy. Soc. Edin ., vol. xxxi., 1910-11, pp. 17-40. 

(3) Berry, R. J. A., and A. W. D. Robertson, “ The Place in Nature of the 
Tasmanian Aboriginal as deduced from a Study of his Calvaria ; Part i., His 
Relations to the Anthropoid Apes, etc.” Proc. Roy. Soc. Edin., vol. xxxi., 1910-11, 
pp. 41-69. 

(4) Cross, K. S., “On a Numerical Determination of the Relative Positions of 
certain Biological Types in the Evolutionary Scale, and of the Relative Values of 
various Cranial Measurements and Indices as Criteria,” Proc. Roy. Soc. Edin., vol. 
xxxi., 1910-11, pp. 70-84. 

(5) Berry, R. J. A., and A. W. D. Robertson, “ Dioptrographic Tracings in 
Eour Normse of Fifty-two Tasmanian Crania,” Trans. Roy. Soc. Viet., vol. v. pt. i., 

1910. 

(6) Berry, R. J. A., “ A Living Descendant of an Extinct (Tasmanian) Race,” 
Proc . Roy. Soc. Viet., vol. xx., N.S., 1907. 

(7) Klaatsch, H., “The Skull of the Australian Aboriginal,” Reports from 
Path. Lab. of Lunacy Dept., N.S.W., vol. i., pt. iii., 1908, pp. 43-167. 

(8) Frederic, J., “ Das Schadelfragment von Stangenas in Schweden,” Zeit. f. 
Morph, u. Antlirop., vol. xi., 1908, p. 317. 

(9) Mollison, Th., “Beitrag zur Kraniologie und Osteologie der Maori,” Zeit. f. 
Moyph. u. Anthrop., vol. xi., 1908, p. 529. 

(10) Turner, Sir William, “The General Characters of the Crania of the 
People of Scotland,” Journ. Anat. and Phys., vol. xxxvii., 1903, pp. 392-408. 



188 



Proceedings of the Royal Society of Edinburgh. [Sess. 

(11) Turner, Sir William, “The Craniology, Racial Affinities, and Descent of 
the Aborigines of Tasmania,” and “ The Aborigines of Tasmania,” Trans. Roy. Soc. 
Edin ., vol. xlvi., 1908, and vol. xlvii., 1910. 

(12) Basedow, H., “Der Tasmanierschadel, ein Insulartypus,” Zeit. f. Ethnol ., 
vol. xlii., 1910. 

(13) Alsberg, C. L., “Keuere Probleme der menschlichen Stammesentwicklung,” 
Arch. Rassen- u. Ges.-Biol. , Band iii., p. 28. 

(14) Haddon, A. C., Races of Man and their Distribution , Miller & Co., 
London, 1912. 

(15) Czekanowski, H., “ Yer wandschaf tsbeziehungen der zentralafrikanischen 
Pygmaen,” Korr.-Blatt. d. deutsch. Gesell. Anthrop ., Ethnol. u. Urgeschichte, vol. xlii., 
1910, p. 101. 

(16) Oppenheim, S., “Zur Typologie des Primatencraniums,” Zeit. /. Morph, u . 
Anthrop., vol. xiv., 1911, pp. 1-204. 

(17) Radlauer, C., “Beitrage zur Anthropologie des Kreuzbeines,” Gegenbaur’s 
morph. Jahrbuch , Band xxxviii., 1908, pp. 322-447. 

(18) Klaatsch, “Das Gesichtsskelett der Neandertalrasse und der Australier,”' 
Verb. anat. Ges., 22. Vers., Berlin, 1908, pp. 223-273. 

(19) von Luschan, “ Keuhollandische Typen,” Korr.-Blatt. d. deutsch. Gesell. 
Anthrop ., Ethnol. u. Urgeschichte , vol. xl., 1909. 

(20) Stratz, C. H., “Das Problem der Rasseneinteilung der Menschheit,” 
Arch.f. Anthropoid vol. xxix., 1903, p. 189. 

(21) Schoetensack, O., “Die Bedeutung Australiens fiir die Heranbildung 
des Menschen aus einer niederen Form,” Zeit. f. Ethnol ., Jahrg. xxxiii., 1 901 , 
p. 127. 

(22) Schwalbe, G., “ Uber das Schadelfragment von Briix und seine Bedeutung 
fiir die Urgeschichte des Menschen,” Verhand. des anthrop. Congr. zu Salzburg , 
August 1905. 

(23) Klaatsch, H., “Ergebnisse meiner australischen Reise,” Korr.-Blatt. d . 
deutsch. Gesell. Anthrop ., Ethnol. u. Urgeschichte , vol. xxxviii., 1907. 

(24) Wetzel, G., “Die Wirbelsaule der Australier. Erste Mitteilung : Das 
Volumen der knochernen Wirbelsaule und ihre Abschnitte,” Zeit. f. Morph, u. 
Anthrop., vol. xii., 1909. 

(25) Biasutti, R., “ I Tasmaniani come forma d’ Isolamento Geografico,” Arch. 
V Antropol., vol. xl. p. 108. 

(26) Sergi, G., “ Tasmanier und Australier. ( Hesperanthropus tasmanianus, 
spec .),” Archiv f. Anthrop., Neue Folge, Band xi., 1912, p. 201. 

(27) Buchner, L. W. G., “ An Investigation of Fifty-two Tasmanian Crania by 
Klaatsch’s Craniotrigonometrical Methods,” and “A Study of the Prognathism of 
the Tasmanian Aboriginal,” Proc. Roy. Soc. Viet., vol. xxv., 1912 ; also the “Curva- 
ture Indices of the Tasmanian Aboriginal Cranium,” ready for publication. 

(28) Topinard, P., Anthropology, Chapman & Hall, London, 1890. 

(29) Ewart, J. Cossar, “Discussion on Heredity in Disease,” Scot. Med. and 
Surg. Journ., vol. vi., 1900, p. 308. 

(30) Lapicque and Baudouin, Discussion on Zaborowki’s “ Metis d’Australien 
et d’ Anglais,” Bull. Soc. d’ Anthrop., 5th series, vol. viii. p. 384. 



1913-14.] The Place in Nature of the Tasmanian Aboriginal. 189 

(31) Kruger-Kelmar, P., Beitrdge zur vergleichenden Ethnologie und Anthro- 
pologie der Neuhollander, Polynesier und Melanesier , Inaug. Diss. Gottingen, 1905. 

(32) Mathew, Eaglehawk and Grow , David Nntt, London, 1899. 

(33) von Luschan, “ Zur Stellung der Tasmanier in anthropologischen System,” 
Zeit.f . Ethnol., Jahrg. xliii., 1911, p. 287. 

(34) Sofer, L., “ Uber die Plastizitat der menschlichen Passe,” Arch. Rassen- u. 
Ges.-Biol., Jahrg. v., p. 660. 

(35) Doncaster, Heredity , Cambridge University Press, 1911. 



{Issued separately April 29, 1914.) 



190 Proceedings of the Royal Society of Edinburgh. [Sess. 



XIII. — A Chemical Examination of the Organic Matter in Oil- 
Shales. By John B. Robertson, M.A., B.Sc., Carnegie Scholar. 
Communicated by Dr J. S. Flett, F.R.S. 

(MS. received February 28, 1914. Read March 16, 1914.) 



Historical. 

Investigations into the nature of the organic matter in oil-shales began 
at the time of the famous Torbanehill case in 1854, when experts attempted 
to settle the question as to whether the substance known as “ Torbanite ” 
or “ Boghead Mineral ” was a coal or an oil-shale. Several witnesses at the 
trial (Gillespie v. Russel, Session Papers , 1854) maintained that the oil- 
producing material in the Mineral was of organic origin, while others 
pronounced it to be bituminous and produced by subaqueous eruptions. 
T. S. Traill, M.D., proposed for the Boghead Mineral the name “ Bitumenite,” 
as it seemed to him to “ consist of much bitumen, mingled with earthy 
matter” {Trans. Roy. Soc. Edin., 1857, xxi. p. 7). Dr Redfern (Quart. 
Journ. Micros. Soc., 1855, x. pp. 118-119), on the other hand, supposed the 
round orange-yellow bodies which occur in torbanite to have had their origin 
in “ a mass of vegetable cells and tissues which have been disintegrated and 
otherwise changed by maceration, pressure, and chemical action, and 
subsequently solidified.” C. E. Bertrand and B. Renault (Bull. Soc. Hist. 
Nat. Autun, 1892-3) on microscopic examination have classed these bodies 
as the remains of gelatinous algae which have been altered by bacterial 
action. They ascribe the genus “ Pila ” to those occurring in the northern 
and “Reinschia” to those found in the southern hemisphere, class the 
bacteria as “ micrococci,” and represent the transformation of the vegetable 
matter by the equation 

C 12 H 20 Oio = 2C 2 H 3 + 5C0 2 + 3CH 4 + 2H. 

This equation is purely empirical, although no doubt carbon dioxide, 
methane, and hydrogen are products of bacterial action upon organic matter. 
Recently this view has been disputed by E. C. Jeffrey (Rhodora, vol. xi. 
p. 61), who has subjected bogheads to a chemical treatment with nitric 
and hydrofluoric acids before making sections, and has affirmed that 
“ the so-called algae ” are in reality “ the strongly sculptured megaspores 
of vascular cryptogams.” Dr W. Scheithauer (Oil-Shales and Tars, 1913) 



191 



1913-14.] The Organic Matter in Oil- Shales. 

expresses the opinion that the remains of dead animals form part of the 
organic material. This view is discussed later. 

Lastly, J. Schuster (. Neues Jahrbuch f Mineralogie, 1912, Bd. ii. p. 33) 
objects to the algal theory, and states that the yellow bodies are in some 
cases concretions of resin, and in others spherulites of silica, calcspar, or 
siderite. 

Little chemical work has been done on the subject beyond a few 
ultimate analyses for purposes of the above-mentioned trial. D. R. Steuart 
(' Oil-Shales of the Lothians, 1912, p. 164) prepared artificial shale from 
lycopodium dust and Florida fuller’s earth, and obtained from it on distilla- 
tion oil and ammonia in quantities similar to those obtained from torbanite. 
He also pointed out that there is very little in torbanite or in ordinary oil- 
shales which can be extracted by petroleum spirit, benzene, carbon di- 
sulphide, or ether, and that therefore the substance cannot be of the nature 
of petroleum, bitumen, or resin. 

Experimental. 

In order to determine whether the organic matter varied in composition, 
and, if so, what was the nature and extent of the variation, ultimate analyses 
were made of thirteen samples of oil -shales. The methods of analysis used 
were the same as those employed by Strahan and Pollard in their analyses 
of coals ( The Coals of South Wales, 1908, p. 6), except in the case of 
carbon and hydrogen determinations, where Walker and Blackadder’s 
modification of the Dennstedt combustion furnace was used. The samples 
were powdered in an agate mortar until sufficiently fine to pass through a 
90-mesh sieve, then dried in a toluene-bath at 105°-107° C. for an hour. 
No boat was used in the combustions, the powdered shale being mixed with 
the copper oxide. The ash was determined separately by igniting the shale 
in a muffle at bright red heat. 

The Kjeldahl method was employed for the nitrogen estimations, a gram 
of shale being used for each determination. The sulphur was estimated 
by heating one gram of the shale with five grams of sodium carbonate in 
a muffle till all the carbon was burned, digesting with warm water, filtering, 
acidifying the filtrate with hydrochloric acid (after the addition of 10 c.c. 
bromine solution to secure complete oxidation), and precipitating the 
sulphate formed with barium chloride. 

It was found that a slight correction was necessary in the hydrogen and 
ash determinations, there being present in the shales hydrous minerals from 
which the water was not expelled at 105° C. The amount of this water 
was estimated by heating a weighed quantity of the shale to a temperature 



192 Proceedings of the Royal Society of Edinburgh. [Sess. 



between 200° and 250° C. in a current of dry nitrogen, and collecting the 
water evolved in a calcium chloride tube. Little or no oil was given off 
at this temperature, but to secure that none was retained in the calcium 
chloride tube a current of dry air was passed through it for twenty minutes 
after each experiment. In a distillation of torbanite under a pressure of 
1 mm., no perceptible quantity of oil was produced until a temperature of 
380° C. had been attained by means of an electric furnace. The correction 
thus applied in no case exceeded 0T5 deduction from the hydrogen per- 
centage, or L35 addition to the ash percentage. The detailed analyses are 
given below along with the works’ yield of oil and ammonium sulphate 
where these are known. The samples of Dunnet shale are from a bore at 
Broxburn, each one representing one foot of the seam in vertical thickness 
from the top downwards. The last two analyses are those of specimens of 
“ burnt ” shales occupying the positions of the “ Maybrick ” and “ Curly ” 
seams of the Pumpherston shales in a bore at Knightsbridge, and described 
by R. G. Carruthers ( Oil-Shales of the Lothians, 1912, p. 88). He puts 
forward the theory that these shales have been “ burnt ” or rendered useless 
not through the proximity of any igneous rock, but through the oil having 
been distilled off from them by the heat evolved from the oxidation of 
pyrites dust in the underlying tuff beds. 

The relatively high percentage of oxygen in sample 12 might be con- 
sidered to lend support to this theory, but this is somewhat negatived by 
the much lower oxygen percentage in sample 13. The high nitrogen 
percentages in each show, however, that whatever changes the shale has 
undergone, the nitrogenous matter has heen the last to be affected. 

List of Shales Analysed. 

1. Dunnet — Top foot (Broxburn). 

2. ,, 2nd „ 

3. „ 3rd „ 

4. ,, 4th 

5. „ 5th „ 

6. „ 6th „ 

7. Camps — Flat portion (Pumpherston). 

8. Camps — Inclined portion (Pumpherston). 

9. Broxburn (Pumpherston). 

10. Torbanite (Armadale). 

11. Australian Commonwealth. 

12. “ Burnt ” Shale — “ Maybrick ” (Knightsbridge). 

13. “ Burnt ” Shale — “ Curly ” (Knightsbridge). 



1913 - 14 .] The Organic Matter in Oil-Shales. 



193 



Data of Analyses. 

I. — Determination op Carbon and Hydrogen. 



No. of 
Shale. 


Weight 

taken. 


C0 2 

found. 


H 2 0 

found. 


Carbon 
per cent. 


Hydrogen 
per cent. 


Carbon 
per cent. 
(Average.) 


Hydrogen 
per cent. 
(Average.) 


1 (a) 


•6309 


•2347 


•0924 


10-15 


1-63 






(b) 


•5657 


•2134 


•0838 


10-29 


1-65 


10*22 


1-64 


2 (a) 


•6226 


•2869 


•0953 


12-57 


1-70 






(b) 


•4704 




•0720 




1-70 






(c) 


•4052 


•1873 


•0643 


12-61 


1-76 


12-59 


1-72 


3 (a) 


•3415 


•2024 


•0689 


16-16 


2-24 






(b) 


•3374 


•1983 


•0681 


16-03 


2-24 


16-09 


2‘24 


4(a) 


•2938 


•1999 


•0660 


18-52 


2-50 






(b) 


•3521 




•0786 




2-48 






(c) 


•3303 


•2233 


•0729 


18-44 


2-45 


18*48 


2-48 


5 (a) 


•3386 


•2422 


•0769 


19-51 


2-52 






(b) 


•3208 


•2264 


•0750 


19-25 


2-60 






(c) 


•3464 


•2512 


•0780 


19-77 


2-50 


19-51 


2-54 


6 (a) 


•5936 


•3546 


•1171 


16-29 


2-19 






(b) 


•3781 




•0781 




2-30 






(c) 


•3575 




•0744 




2-31 






(d) 


•3590 


•2165 


•0729 


16**44 


2;26 


16-36 


2-26 


7 (a) 


•2450 


•1979 




2203 








(b) 


•2474 


•1986 


•0653 


21-90 


2-93 


21-96 


2-93 


8 (a) 


•3558 


•1318 


•0567 


10-10 


1-77 






(b) 


•4118 


•1534 


•0655 


10-16 


1-77 


10*13 


1*77 


9 (a) 


•3694 


•3382 


•1260 


24-97 


3-79 






(b) 


•2831 


■2576 


•0967 


24-80 


3-79 


24-88 


379 


10 (a) 


•1160 


•2780 


•0861 


65-34 


8-25 






(b) 


•1181 


•2864 




66-13 








(c) 


•1016 


•2447 




65-69 








(d) 


•0970 




•0735 




8-42 






(«) 


•0988 




•0746 




8-39 


65-72 


8-35 


11 (a) 


0885 




•0626 




7-86 






(b) 


•0900 


•2093 




63-60 








(o) 


•0851 




•0601 




7-85 






i (d) 


•0856 


•1994 




63-56 




63-58 


7-86 


12 (a) 


•5025 


•1085 


•0451 


5-89 


Too 






(b) 


•9977 


•2193 


•0843 


5-99 


0-94 






(c) 


•5985 


•1333 


•0525 


6-07 


0-97 


5-98 


0-97 


13 (a) 


•8383 


•2459 


■0921 


8-00 


1-22 






(b) 


•6971 


•2123 


•0830 


8-30 


1-32 


8-15 


1-27 



YOL. XXXIY. 



13 



194 



Proceedings of the Royal Society of Edinburgh. 



II. — Determination of Nitrogen. 



No. of Shale. 


Weight 

taken. 


Nitrogen 

found. 


Nitrogen 
per cent. 


Nitrogen 
per cent. 
(Average.) 


1(a) 


•9984 


•004766 


0*48 




w 


1*0008 


•005057 


0-51 


0*49 


2 (a) 


1-0025 


•005538 


0-55 




(b) 


*9969 


•005104 


0-51 


0-53 


3(a) 


1-0046 


•006161 


0 61 




• (6) 


•9999 


005989 


0-60 


0*61 


4 (a) 


•9976 


•006810 


0-68 




(b) 


1-0015 


•006569 


0-66 


0*67 


5 (a) 


1-0019 


•006746 


0-67 




W 


1-0020 


•007100 


0-71 


0-69 


6(a) 


1-0017 


•005925 


0-59 




(6) 


1-0020 


•006166 


0-62 


0-60 


7(a) 


1-0031 


•006182 


0-62 




(&) 


1-0033 


•006907 


069 


0*65 


8 (a) 


1-0011 


•005361 


0-54 




(6) 


•9971 


•005313 


0-53 


0*53 


9(a) 


•9971 


•006585 


0-66 




(b) 


•7123 


•005071 


0-71 


0*68 


10 (a) 


•9985 


•006311 


0-63 


• • • 


(6) 


1-0039 


•006327 


0-63 


0-63 


11(a) 


•9984 


•007986 


0-80 


. . . 


(b) 


1-0009 


•008147 


0-81 


0-81 


12 (a) 


1-0004 


•007736 


0-77 


• . . 


W 


•9946 


•007223 


0-73 


0-75 


13 


1-0001 


•01233 


1-23 





III. — Determination of Sulphur. 



No. of Shale. 


Weight 

taken. 


Barium 

Sulphate 

found. 


Sulphur 
per cent. 


Sulphur 
per cent. 
(Average.) 


1 (a) 


•997 


•0682 


0-94 


... 


(b) 


1-005 


•0659 


0-90 


0-92 


2 (a) 


1-004 


•0871 


1-19 




(b) 


•998 


•0860 


1-18 


lib 


3(a) 


1-005 


•1277 


1-75 




(b) 


1-005 


•1262 


1-73 


1-74 


4(a) 


1-003 


•0953 


1-31 




(b) 


1-003 


•0953 


1-31 


1*31 


5 (a) 


1-006 


•0992 


1-36 




(b) 


1-006 


•0990 


1-36 


1*3*6 


6(a) 


•998 


•1982 


2-73 




(6) 


1-000 


•1970 


2-71 


2*72 


7(a) 


•998 


•0914 


1-26 




(b) 


•997 


•0912 


1-26 


1-26 


8 (a) 


1-002 


•0382 


0-52 




<b) 


1-004 


•0395 


0-54 


0-53 


9 (a) 


1-005 


•0589 


0-81 




(b) 


1-004 


•0583 


0-80 


0*80 


10 (a) 


1-004 


•0196 


0-27 




(b) 


•999 


•0213 


0-29 


0*28 


11 (a) 


1-002 


•0285 


0-39 




(b) 


•997 


•0336 


0-46 


0-43 


12 (a) 


•997 


•0511 


0-70 




(b) 


1-002 


•0483 


0-66 


0*68 


13 


1-002 


•1716 


2*35 





[Sess. 



1913-14.] The Organic Matter in Oil-Shales. 



195 



IV. — Determination of Ash. 



No. of Shale. 


Weight 

taken. 


I 

Ash. 


Ash 

per cent. 


1 

Ash 

per cent. 
(Average.) 


1(a) 


•2025 


•1655 


81-73 




(&) 


•1995 


•1629 


81*65 


81*69 


2(a) 


•2054 


•1629 


79-30 




W 


•1965 


•1553 


79-02 


79-16 


3 (a) 


•2013 


•1514 


75-21 




W 


•1998 


•1496 


74-87 


75*04 


4(a) 


•2032 


•1506 


74-11 




(6) 


•1982 


•1469 


74-13 


74*12 


5 (a) 


•2027 


1455 


71-78 




W 


•1974 


•1430 


72-43 


72-11 


6(a) 


•2002 


•1493 


74-58 




(6) 


•2009 


•1499 


74*64 


74-61 


7(a) 


•2050 


•1413 


68-92 




(6) 


•2070 


•1418 


68-48 


68-70 


8(a) 


•2023 


•1674 


82-75 




(6) 


•1962 


•1612 


82-15 


82-45 


9(a) 


•1997 


•1215 


60-81 




(6) 


•1997 


•1216 


60-87 


60-84 


10 (a) 


•6994 


•1237 


17*68 




(&) 


•6998 


•1234 


17-63 


17-66 


11(a) 


*7036 


•1581 


22-47 




(6) 


*7063 


•1586 


22-46 


22-47 


12 (a) 


•2009 


•1669 


83-10 




W 


•2007 


•1659 


82-68 


82-89 


13 (a) 


•1961 


•1653 


84*29 




(6) 


•1963 


•1656 


8435 


84-32 



V. — Correction for Hydrogen Minerals. 



N T o. of Shale. 


Weight 

taken. 


Weight 
of Water. 


Hydrogen 
per cent, to 
be deducted. 


Ash 

per cent, to 
be deducted. 


1 


1-1199 


•0094 


0*09 


0-84 


2 


■9110 


•0034 


0-04 


0-37 


3 


1-0799 


•0054 


0-06 


0-50 


4 


•9638 


■0038 


0-04 


0-39 


5 


•8944 


•0048 


0-06 


0-54 


6 


1-0090 


•0046 


0-05 


0-46 


7 


•6948 


•0042 


007 


0-60 


8 


1-0027 


•0065 


0-07 


063 


9 


•5275 


•0056 


0-12 


1-06 


10 


•5310 


•0038 


0-08 


0-72 


11 


•6088 


•0030 


005 


0-49 


12 


1-0041 


•0135 


0-15 


1-35 


13 


1-0303 


•0107 


012 


1-04 



General Results of Analyses. 



196 



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1913-14.] The Organic Matter in Oil-Shales. 



197 



Discussion of Analytical Data. 

Strahan and Pollard have adopted the “ carbon-hydrogen ratio ” (C/H) 
as a basis for the classification of coals, and have found it to vary from 12 -9 
in “ per-bituminous ” coals to upwards of 30 in anthracites. A variation in 
a smaller degree can be seen in the shales, the limits in the above analyses 
being 5*96 and 8*14. In all cases the ratio is lower than in the coals. The 
analyses show that the organic matter varies considerably in constitution 
in different shales. The most interesting fact revealed, however, is the 
connection between the carbon-hydrogen ratio and the yield of oil. The 
law would seem to be established that the yield of oil varies directly as the 
percentage of organic matter , and inversely as a function of the carbon- 
hydrogen ratio. This is strikingly shown by comparing analyses 3 and 4, 
where the same oil yield is obtained from the two samples, the excess of 
2*4 per cent, of carbon in 4 being neutralised by its higher carbon-hydrogen 
ratio of 7*57 as compared with 7*38 in 3. It is still more evident on a 
comparison of Nos. 7 and 8, where the oil yield in the latter is actually 1*5 
gallons more than in the former, although the carbon percentages are 10*13 
and 21*96 respectively, the explanation being that in 8 the carbon-hydrogen 
ratio is only 5*96, whereas in 7 it is comparatively high, viz. 7*68. It is 
thus shown that the all-important factor in shale analysis is the determina- 
tion of the relative percentage of hydrogen present, and that an approxi- 
mate analysis of a sample into volatile matter, coke, and ash may not shed 
so much light on its oil-producing properties as an ultimate carbon and 
hydrogen analysis. 

Action of Solvents on Shale. 

Mention has already been made of the fact that very little is extracted 
from shale by the common organic solvents. Dichlorhydrin, a high boiling 
solvent (b.p. 174° C.) was tried without success, but pyridine (b.p. 117° C.) 
was found to be an effective solvent. 

The Committee on Explosions in Mines (2nd Report, 1912) has investi- 
gated the solubility of coals in pyridine and shown that quantities of extract 
may be obtained varying from 3*7 to 38*8 per cent, on the ash-free dry coal. 
Torbanite and Broxburn shale were both completely extracted with pyridine, 
and it was found that 4*92 and 3*29 per cent, respectively of the ash-free 
dry shale was dissolved. If then, as is suggested in the report of the above 
committee, the extracted material represents the resinous part of the coal 
(the small percentages are from semi-bituminous, and the high from bitu- 
minous, coals), it is evident that only a very small portion of the organic 
matter in shale is of a resinous character. 



198 Proceedings of the Royal Society of Edinburgh. [Sess, 

The extracts were obtained by treating the finely divided shale with 
pyridine in a Soxhlet extraction apparatus until the solvent siphoning over 
was no longer coloured, distilling off the pyridine at 60° C. under reduced 
pressure, transferring the semi-solid residue to a watch-glass and drying it 
in a vacuum desiccator over sulphuric acid. The extracts were dark brown 
in colour and showed a tendency to crystallise in radiating needles. They 
gave the following results on analysis : — 



Extract from Torbanite. 



(1) *0864 gave ‘0694 H 9 0 and *2590 C0 2 

(2) -0808 „ -0653 | „ -2467 „ 

(3) -0679 „ -0560 „ *2042 „ 

(4) *0684 „ -2088 „ 



0 = 81-75 
C = 83-26 
0 = 82-01 
0 = 83-26 



Average . . C = 82*57 per cent. 

*5031 gave "005023 N 2 N = l - 00 per cent. 

•502 „ -0138 BaS0 4 S = -38 „ 



H = 8-93 
H = 8-98 
H = 9-16 



H = 9-02 per cent. 



Extract from Broxburn Shale. 



•0726 gave -0768 H 2 0 and -2196 C0 2 

From Torbanite. 

0 82-57 
H 9-02 
N 1-00 
S -38 
(by difference) O 7*03 



100-00 



0 = 82*49 per cent. H = 11 -75 per cent. 

From Broxburn Shale. 

C 82-49 
H 11-75 

S > not estimated. 



These extracts are in all probability mixtures, as small proportions of 
them are dissolved by alcohol, benzene, etc. 



Action of Nitric Acid on Shales. 

Carrick Anderson (Jour. Soc. Chem. Ind., 1898, vol. xvii. p. 1018) 
described the action of nitric acid on coals, and gave analyses of the 
products obtained from seven different samples. These products are acids, 
and the product from any coal is always of constant composition provided 
an excess of acid is used. As it seemed possible that a comparison of these 
acids with any similar compounds which might be obtained from shales and 
other substances might throw some light on the origin and nature of the 
organic matter in shale, an endeavour was made to obtain similar deri- 
vatives from the following: — (1) Torbanite, (2) Broxburn shale, (3) New- 
battle cannel coal, (4) peat from Glenfalloch, (5) lycopodium spore dust, 
and (6) an organic sludge consisting mainly of decomposed leaf and root 
remains, microscopic algse, diatoms, and bacteria. From all of these, except 



199 



1913 - 14 .] The Organic Matter in Oil-Shales. 

the last, derivatives were obtained. In the case of the organic sludge, 
oxidation, even although moderated by careful cooling, was sufficiently 
vigorous to change most of the oxidisable material into oxalic acid and 
carbon dioxide. The finely divided material was evaporated to dryness 
with excess of concentrated nitric acid, the solid residue treated with 
ammonia solution, filtered, and the acid precipitated from the filtrate by the 
addition of dilute hydrochloric acid. This precipitate was filtered, washed 
with water till free from chloride, and dried in a vacuum over sulphuric 
acid. In the experiments with lycopodium and with peat the first action 
had to be moderated by cooling. The substance obtained from lycopodium 
was light brown in colour and gummy. All the other preparations were 
more or less dark brown in colour, hard, and brittle. They all contained 
traces of sulphur and a small amount of ash. In no case was the whole of 
the organic matter converted into acid, there being formed in all the 
preparations a larger or smaller quantity of oxalic acid. A small quantity 
of powdered torbanite, after being repeatedly treated with nitric acid and 
ammonia as above, was examined under the microscope. The residue was 
found to consist of inorganic materials, with here and there particles of 
organic matter which had been prevented from going into solution through 
being enveloped in inorganic materials. These acids form insoluble salts 
with some metallic radicals such as silver, lead, copper, iron, cobalt, and 
barium. They gave the following figures on analysis (neglecting traces of 
sulphur and ash) : — 

Acid from Torbanite. 

(1) -0784 gave *0533 H 2 0 and T765 C0 2 0 = 61*39 

(2) -0964 „ -0632 „ „ *2162 „ 0 = 61*13 

Average . . C = 61*26 per cent. 

(1) *5993 gave *02189 N 2 N = 4*38 

(2) *4993 „ *02181 N 2 N = 4*37 

Average . . N = 4*37 per cent. 

Acid from Broxburn Shale. 

(1) *0937 gave *0576 H 2 0 and *2040 C0 9 0 = 59-38 

(2) -0897 „ -0533 „ 

(3) -0947 *2079 „ 0 = 59*87 

Average . . 0 = 59*62 per cent. 

*5065 gave *02175 N 2 N = 4*29 per cent. 

Acid from Cannel Coal. 

(1) -0991 gave -0474 H 2 0 and *1934 C0 2 0 = 53*22 

(2) *1146 „ *0576 „ „ *2270 „ 0 = 54*01 

Average . . 0 = 53*61 per cent. 

N = 3*92 per cent. 



= 7*55 
= 7*29 



7*42 per cent. 



H = 6*83 
H = 6*60 



H = 6*72 per cent. 



31 



*5008 gave *01963 N 2 



200 



Proceedings of the Royal Society of Edinburgh. [Sess. 



Acid from Peat. 

•0557 gave *0274 H 2 0 and ’1081 C0 2 0 = 52*93 per cent. H = 5*47 per cent. 

•0976 „ *004477 N 2 N = 4-59 per cent. 

Acid from Lycopodium. 

(1) *1051 gave -0891 H 9 0 and -2334 C0 2 C = 60 56 H = 9*42 

(2) -1006 „ *0848 „ *2204 „ C = 59*75 H = 9*37 



Average . . C = 60 ’15 per cent. H = 9-39 per cent. 

(1) -4966 gave *01904 N 2 N = 3*83 

(2) *5106 „ *01916 „ N=3*77 

Average . . N = 3*80 per cent. 



Acids obtained from Shales, etc. 





Torbanite. 


Broxburn 

Shale. 


Cannel Coal. 


Peat. 


Lycopodium. 


c 


61*26 


59*62 


53*61 


52*93 


60*15 


H 


7*42 


6*72 


5*44 


5*47 


9*39 


N 


4*37 


4*29 


3*92 


4*59 


3*80 


O 

(by difference) 


26*95 


29*37 


37*03 


37*01 


26*66 


100*00 


100*00 


100*00 


100*00 


100*00 



The estimation of the metallic radicals in the silver and ammonia salts 
of the acids from torbanite and Broxburn shale confirm these analyses, and 
point to the empirical formulae : — 

From : — 

Torbanite. Broxburn Shale. Cannel Coal. Peat. Lycopodium. 

c 16 h 24 no 5 c 16 h 22 no 6 c 16 h 19 no 8 c 13 h 17 no 7 c 19 h 35 no 6 

The empirical formulae calculated from Carrick Anderson’s coal-acid 
analyses are : — C 14 H 9 N0 6 (Ell) ; C 15 H 9 N0 5 (Splint) ; C 15 H 9 N0 5 (Gas) ; 
C l7 H 10 NO 7 (Virgin); C l7 H 10 NO 6 (Lower Drumgray); C 16 H 10 NO 6 (Bannock- 
burn Main); and C 21 H 13 N0 8 (Kilsyth Coking). 

These substances, which are evidently all of the same nature, can be 
arranged into a series commencing with lycopodium acid where the 
hydrogen is relatively highest, and passing through torbanite, Broxburn 
shale, peat, and cannel coal-acids to ordinary coal-acids where the hydrogen 
is relatively lowest. It being recognised that the first and last terms of the 
series represent derivatives of pure vegetable matter and of highly meta- 
morphosed vegetable matter respectively, the probable conclusion is that 
the intermediate terms represent different stages in the alteration of 
vegetable matter. This does not, of course, infer that the process of change 



201 



] 913-14.] The Organic Matter in Oil- Shales. 

has been through the above steps, as no doubt the different substances 
experimented on were produced under different conditions of moisture, 
temperature, bacterial action, etc. Each product may, however, represent 
the end point of a definite series of reactions produced by definite condi- 
tions. The close relationship between the formulae for the shale acids, peat 
acid, and cannel coal-acid may signify a definite stopping-place in the 
process of decomposition of vegetable matter, the carbon having increased 
at the expense of the hydrogen and highly complex substances having been 
formed. 

There would seem to be no experimental ground for concluding that 
animal remains are mingled with this vegetable product, as on careful 
examination no trace of phosphates could be found in samples of torbanite, 
Broxburn, Camps, or Dunnet shales, and as the lime in the ash of shales is 
low, varying from a “ trace ” to P55 per cent. ( Oil-Shales of the Lothians, 
1912, pp. 159, 161). 

Summary. 

1. The carbon-hydrogen ratio varies in the oil-shales from 6 to 8 and 
over. The lower this ratio the larger is the amount of oil produced from a 
definite percentage of organic matter. The carbon-hydrogen ratio is, in 
all the shales examined, lower than that of ordinary bituminous coals. 
The oil-shales are thus distinct from coals, although the richer varieties 
may approach cannel coals in properties. 

2. There is but little resinous substance in oil-shales, the main bulk of 
the organic material being insoluble in organic solvents. 

3. The organic substance in oil-shale is a decomposition product of 
vegetable matter (originally algse, spores, or simply concretions of macerated 
organic material) similar in nature to that found in peat and in cannel 
coal, and produced by a definite combination of external conditions. 

In conclusion, I desire to thank Dr Flett for suggesting the lines of this 
research ; Mr R. G. Carruthers, Mr D. Tait, Mr D. R. Steuart, F.I.C., Mr Wm. 
Caldwell, and Messrs Muir & Co. for assistance in securing samples ; and 
Professor Walker, Dr J. E. Mackenzie, Dr Gordon, and Dr Campbell for 
their advice, assistance, and criticism throughout the research. 



{Issued seyaralely July 15, 1914.) 



202 Proceedings of the Boyal Society of Edinburgh. [Sess. 



XIV. — Notes on the Atmospheric Electrical Potential Gradient in 
the Industrial Districts around Leeds. By Dan. W. Steuart and 
Ingvar Jorgensen. Communicated by James A. S. Watson, B.Sc. 

(MS. received February 13, 1914. Read March 16, 1914.) 

The atmosphere of industrial districts is characterised by the pollution 
which it receives from smoke, comprising solid matters like carbon, tar, 
and mineral ash, and gaseous constituents such as S0 2 and C0 2 . 

Much work has now been done with regard to the ionisation of gases 
by various means.* Small ions, with a velocity of 1*6 cms. per second in 
an electric field of 1 volt per cm., have long been known to exist in the 
atmosphere. About ten years ago Langevin,f working in Paris, demonstrated 
the presence of large ions in addition, velocity 1/3000 cm. per second. 
M'Clelland and Kennedy J described the formation of large ions in the 
products of combustion, and later Kennedy, § comparing town and country 
air, found in town air (Dublin) a larger number of ions, due to combustion 
processes ; the large ions being increased, and to some extent at the expense 
of the small ones. Aitken [| has shown that the various products of 
combustion include nuclei of condensation and of spontaneous condensa- 
tion, due largely to the presence of sulphur in the fuel. As the envelope 
which transforms small into large ions often consists of water, these two 
sets of results may be correlated to some extent. Eve,H for example, 
concluded that dust, smoke, or mist in air causes a transformation of small 
into large ions. Several sizes of ions are now known to exist in air, 
commencing with the small ions and with decreasing velocities as the 
size increases.** 

The foregoing researches indicate that ionisation by combustion and 
the presence of combustion products in the air may be essential factors in 
the phenomena of atmospheric electricity in industrial districts. 

The following notes deal with measurements of potential gradients 

* J. J. Thomson, Conduction of Electricity through Gases. H. A. Wilson, Electrical 
Properties of Flames and Incandescent Solids , 1912. 

t Comptes Rendus, 1905, p. 233. 

J Proc. Roy. Irish Acad., 1912, xxx., A, No. 5. 

§ Proc. Roy. Irish Acad., 1913, xxxii., A, No. 1. 

|| These Proceedings , 1912, xxxii., Part 2, No. 16, and earlier. 

IT Phil. Mag., ccxxxv. p. 257. 

** Cf. Sutherland, Phil. Mag., 1909, p. 341. 



1913-14.] Atmospheric Electrical Potential Gradient. 203 

in such districts in the neighbourhood of Leeds, and with a few experi- 
ments designed to suggest an explanation of certain abnormalities, as 
compared with previous records. Our apparatus * comprised a Lutz 
flame collector on an ebonite rod, an Exner electrometer for measuring 
potential differences to 800 volts, and a Braun electrometer for read- 
ings over 800. All measurements were made at a height of 1 metre 
from earth. 

Curve A . — These measurements were made on a grass field near 
Kirkstall Forge, Leeds. The wind was blowing from the forge chimneys 
about 150 yards away ; the tops of the chimneys being a little below the 



A. 




level of the instruments. During forty minutes the potential gradient 
varied rapidly between 720 and 2200 volts per metre. 

On another day the instruments were 350 yards from these chimneys 
in the same direction, and the smoke caused a variation between 300 
and 2250 during thirty-five minutes. A few hours later, owing to a 
change in the wind, most of the smoke blew somewhat to our right, 
and the variations were in consequence only from 120 to 300 during 
twenty minutes. 

On another occasion we were half a mile from the forge in the same 
direction, and during fifty minutes the reading was never below 630. 
At this same spot, with the same wind direction and on two different 
days, the minimal readings were 390 during ninety minutes and 120 
in twenty minutes, depending on the amount of smoke which reached 
the collector. 

* For the loan of the apparatus we are indebted to Prof. J. H. Priestley. 



204 Proceedings of the Eoyal Society of Edinburgh. [Sess. 



5 : 




With a different wind direction the 
smoke from the forge was rising rapidly 
out of the valley and drifting over a hill. 
At the top of the hill the smoke was still 
mostly going right over our heads,** and 
the readings in forty minutes were from 
140 to 220, while 50 yards down the slope 
during thirty minutes the variations were 
from 75 to 130. 

Curve B was taken near Garforth 
colliery, seven miles east of Leeds. It 
shows readings taken at distances of 100, 
350, and 880 yards from a tall chimney 
when the wind was blowing smoke towards 
the instruments. About two hours after 
the last reading was made the instruments 
were taken to a position about half a mile 
to the windward of the chimney, and 
during twenty minutes the reading was 
never above 135. 

It will be seen that fresh smoke reach- 
ing the collector caused an increase in the 
positive potential gradient. We commonly 
got readings of over 800 volts at distances 
over a mile from large chimneys. The 
interpretation of these measurements is 
slightly complicated owing to the ordinary 
variations in the potential gradient due to 
other causes. It is consequently more con- 
venient to study the effect of smoke by 
means of passing trains, as in that case the 
smoke effect is limited to a definite interval 
of time, as will be seen from the following 
curve. 

Curve C . — A slight wind was blowing 
from a railway 300 to 400 yards away 
(wind direction roughly at right angles 
to the railway). The ground level was 
below the level of the railway, and smoke 
from trains was wafted slowly down to 



0001 



205 



1913-14.] Atmospheric Electrical Potential Gradient. 




ex: 



A 




VOLTS PER METRE. 



°o 



cvj 



206 



Proceedings of the Royal Society of Edinburgh. [Sess. 

the instruments. The passage of a train is marked, and the effect of its 
smoke came several minutes later. 



Train 1. No visible smoke. 

„ 2. A little white smoke. 

„ 3. Copious white smoke. 

„ 4. No visible smoke. 

„ 5. No visible smoke. 

„ 6. No visible smoke. 



7. Two trains 



(a) Dense black smoke. 

( b ) No visible smoke. 



No effect was recorded, probably owing to some slight variation in the 
wind. 



Train 8. White smoke. 
„ 9. White smoke. 






10. Two trains 



(a) Dense black smoke. 

( b ) No visible smoke. 



In the case of the white smoke the colour is due to moisture, and all 
whiteness had generally disappeared long before the smoke reached the 
instruments. Wilson concluded that the positive ions in a bunsen flame 
consist of charged molecules of the gases present. Similarly solid particles 
do not seem to be necessary for the carriage of the positive charge in 
smoke. 

These potential gradient measurements confirm the conclusions of others 
that by combustion a considerable amount of ionisation is produced ; but 
as the effect is always to produce an increase of the positive potential 
gradient, more positive than negative ions may be formed. 

By burning considerable quantities of benzene, methylated spirits, and 
sulphur, separately and simultaneously in the open, at distances up to 
25 yards from the collector, and under various meteorological conditions we 
were unable to reproduce the smoke effect. On burning these substances 
in the laboratory we found that the cooled combustion gases, in each case, 
contained both positive and negative ions,* and in approximately equal 
numbers as far as we could gauge with the apparatus at our disposal. 
The mixed products of combustion would contain C0 2 , S0 2 , S0 3 , carbon 
particles, water vapour, and nuclei both of condensation and of charge, 
as in the case of coal smoke. 

We consider, therefore, that the ionisation giving rise to the largely 



* L. Bloeh, Annates de Ghemie et de Physique, xxii. and xxiii. Reoglie and Brizard, 
Comptes Rendus, 1909, p. 146. 



1913-14.] Atmospheric Electrical Potential Gradient. 207 

increased potential gradient must produce many more positive than 
negative ions, due to some characteristic of the mechanism of the com- 
bustions investigated. Such is the case, for example, with ionisation by 
certain incandescent particles at moderately high temperatures.* In the 
cases cited the effluent gases would have been subjected to a temperature 
of perhaps from 600 to over 1000° C.+ 

This work was done during the summers of 1912 and 1913 in connection 
with other smoke experiments being conducted at Leeds University. In 
studying the effects of smoke on plant growth it is very desirable to have 
some means of measuring the concentration of noxious smoke gases in the 
atmosphere, and we hoped that this object might be attained by measure- 
ments of the air potential gradient. It does not seem, however, as if these 
would give much guidance. 



Summary. 

The general effect of products of combustion would be to cause a 
transformation of the small ions of the air into large ions, which, acting 
alone, would tend to decrease the air conductivity. Ionisation by flames, 
however, adds to the number of ions in the air, so that the size of the ions 
might be increased without the conductivity of the air diminishing. In 
the case of the fresh smoke direct from the forge or colliery chimney- 
stalks or railway engines of our experiments, it is suggested that com- 
bustion in the furnaces would result in an ionisation producing more 
positive than negative ions. It is only where similar conditions obtain 
that we should expect such large increases in the positive potential 
gradient, due to smoke, as we have recorded. 

* H. A. Wilson, loc. cit. 

t Rusby, Journal of Franklin Inst., July 1913. 



(. Issued separately July 15, 1914.) 



208 



Proceedings of the Royal Society of Edinburgh. [Sess. 



XY. — On the Hall and the Transverse Thermomagnetic Effects 
and their Temperature Coefficients. By F. Unwin, M.Sc., 
Assistant Lecturer in Physics, Heriot-Watt College, Edinburgh. 
Communicated by Professor F. G. Baily. 

(MS. received May 5, 1914. Read June 15, 1914.) 

Introduction. 

Of the more recent researches on the subject of this paper, mention may 
be made of the work of H. Zahn * on the sralvanomavnetic and thermo- 

O 

magnetic effects in various metals. Zahn has measured these effects in 
many different metals, and has used his results to test the electron theory 
of the properties of metals as developed by P. Drude. He has also 
determined in some cases the temperature variation of the effects. 

The author of the present paper has confined his attention to the 
thermomagnetic transverse effects and the Hall effect. These have been 
measured in magnetic fields of various strengths and at temperatures 
varying over a range of about 100 Centigrade degrees. 

The experiments were carried out with a view to obtaining some light 
on the electron theory, and the ratios of the effects are discussed in relation 
to this theory. 

Definition of the Coefficients of the Effects and the 
Convention with respect to the Signs. 

In accordance with the custom of other workers, the Hall coefficient is 
denoted by R, the Thermomagnetic Temperature Effect by S, and the 
Thermomagnetic Potential Effect by Q. 

The directions of the effects corresponding to positive values of these 
coefficients are indicated by the diagrams (fig. 1) given below; it being 
understood that the magnetic field is in each case directed downwards 
at right angles to the plane of the diagram. 

The value of S is found as usual by calculating the transverse 
temperature difference in a plate 1 cm. broad placed in unit magnetic field, 
when the temperature gradient along the axis is 1° C. per cm. 

The value of Q is found by calculating the transverse E.M.F. (in 
electromagnetic units) under the same conditions. 

* Ann. d. Phys., xiv. p. 886, 1904. 



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MODEL INDEX. 

Schafer, E. A. — On the Existence within the Liver Cells of Channels which can be directly 
injected from the Blood-vessels. Proc. Roy. Soc. Edin., vol. , 1902, pp. 

Cells, Liver, — Intra-cellular Canaliculi in. 

E. A. Schafer. Proc. Roy. Soc. Edin., vol. 

Liver, — Injection within Cells of. 

E. A. Schafer. Proc. Roy, Soc. Edin., vol. 



, 1902, pp. 
, 1902, pp. 



IV 



CONTENTS. 



NO. PAGE 

XIV. Notes on the Atmospheric Electrical Potential Gradient in 
the Industrial Districts around Leeds. By Dan. W. Steuart 
and Ingvar Jorgensen. Communicated by James A. S. 
Watson, B.Sc., ...... 202 

{Issued separately July 15, 1914.) 

XV. On the Hall and the Transverse Thermomagnetic Effects and 
their Temperature Coefficients. By F. Unwin, M.Sc., Assis- 
tant Lecturer in Physics, Heriot-Watt College, Edinburgh. 
Communicated by Professor F. G. Baily, . . . 208 

{Issued separately , 1914.) 



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Part III.] VOL. XXXIV. [PP- 209-371. 



CONTENTS. . 

NO. ' PAGE 

XVI Some Factorable Continuants. By W. H. Metzler, Ph.D., . 223 

{Issued separately September 3, 1914.) 

XVII. The Analytical Study of the Mechanism of Writing. By 
James Drever, M.A., B.Sc. Communicated by Dr 
Alexander Morgan, ..... 230 

(. Issued separately September 3, 1914.) 

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{Issued separately September 4, 1914.) 

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of Four Dimensions. By D. M. Y. Sommerville, M.A., 

D.Sc., Lecturer in Mathematics, University of St Andrews. 

(With a Plate), ...... 253 

{Issued separately September 29, 1914.) 

XX. Changes of Electrical Resistance accompanying Longitudinal 
and Transverse Magnetizations in Iron and Steel. By 
Professor C. G. Knott, D.Sc., .... 259 

{Issued separately December 14, 1914.) 

[' Continued on page iv of Cover . 

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[Continued on page iii of Cover. 



1913-14.] The Hall and Transverse Thermomagnetic Effects. 209 

In the case of the Hall effect, the value of R is calculated for unit 
potential gradient instead of for unit current density, as it would seem that 
the coefficient calculated in this way should be more directly comparable 
with the coefficients S and Q. The value of R, therefore, is the transverse 



R 


s 


Q 


4- 


Warm 


- — 


Electric \ 
Current ^ 




Heat 

Current 




Heat x. 
Current 


— 


Cold 


+ 



Fig. 1. 



E.M.F. (electromagnetic units) in a plate of unit breadth when placed in 
unit magnetic field, the potential gradient along the axis being 1 electro- 
magnetic unit per cm. 

Apparatus. 

The specimen plate, abed (fig. 2), to be tested was soldered to two 
copper lugs L, L, which were themselves soldered to two brass tubes T, T. 
These tubes were fixed to a wooden frame, which served as a support. 

The breadth of the specimen plate was in all cases about 2 cm., and the 
distance between the lugs about 5 cm. The thickness differed for the 
different specimens, but was in all cases less than a millimetre. Wires 
were soldered to the brass tubes to enable an electric current to be sent 
through the plate for the Hall effect measurement. 

Five copper-constantan thermocouples were soldered to the plate at five 
points A, B, C, D, E. The three points E, B, and D were on the axis 
of the plate, while A and C were on a line perpendicular to this axis 
and passing through B. The distances between B and the other points 
were approximately 1 cm., but the actual distances were measured for 
each plate. 

The thermocouples were made of line wire (No. 42 S.W.G.), so as to 
avoid as far as possible any cooling effect due to conduction of heat along 
the wires. 

Two water jackets J, J, 8 cm. by 5 cm. and about 1 mm. thick, were 
placed one on each side of the plate, and were kept at a distance of 0*84 cm. 
apart by brass distance-pieces, thus forming a kind of box enclosing the 

specimen plate. The space between the plate and these jackets was filled 

VOL. xxxiv. 14 



210 



Proceedings of the Royal Society of Edinburgh. [Sess. 



with loosely packed cotton- wool. These jackets were found to be necessary 
in order to bring the plate to a stationary condition as regards temperature. 
In some cases they were supplied with cold water, and in others with steam. 

The electromagnet used was of the “ ironclad ” type, and was designed 
by Professor Baily and built up in the workshops of the Heriot-Watt College. 
The pole-pieces had a maximum diameter of 20 cm. and were coned 
down to a pole face of 5 cm. diameter. Each pole carried an exciting coil 




1/vVJ 



/aA 




of 880 turns, so that with a current of 20 amperes a magneto-motive force 
of 35,200 ampere-turns was obtained. This was found to produce a field 
strength of about 20,000 C.G.S. units. 

Measuring Arrangements. 

The free ends of the wires of the five thermocouples were soldered 
to stouter copper wires, and these junctions were kept in a Thermos flask, 
by which means their temperature was maintained constant for the length 
of time required for the observations. 



1913-14.] The Hall and Transverse Thermomagnetic Effects. 211 

The ten copper wires from this junction box were led to a small 
distributing board (fig. 3). Two similar moving coil galvanometers 
were used, and these were connected to the distributing board through 
the keys P x and P 2 . The measured low resistances S x and S 2 formed 
portions of the galvanometer circuits and served as potentiometer wires. 
They carried currents supplied by the accumulators V 1 and V 2 , and 
regulated by the resistance boxes R x and R 2 . 

One of the measuring circuits was connected to the contacts H and I 




Fig. 3. 

on the distributing board, and the other to the contacts J and K ; the 
galvanometers could thus be easily connected to any of the couples or 
to the separate wires of different couples. 

Method of Observation. 

Thermomagnetic Effects. 

The brass tubes were supplied respectively with aniline vapour and 
steam, or aniline vapour and cold water, or steam and cold water, as the 
case might be, so as to produce the required temperature gradient, and 
the jackets were supplied with cold water or steam according to circum- 
stances. When the plate had attained a steady state, the temperatures at E, 
B, and D were determined by means of the corresponding thermocouples. 



212 



Proceedings of the Eoyal Society of Edinburgh. [Sess. 



The copper wires belonging to the junctions at A and C were then 
connected to one of the galvanometer circuits, and the constantan wires 



of the E.M.F.’s in these two circuits were taken, first when the magnetic 
field was zero, and afterwards with magnetic fields of known strength in 
each direction. The thermoelectric force between copper and constantan 
at various temperatures being known from the results of a special 
experiment, the transverse temperature difference and the transverse 
potential difference due to the magnetic field could then be calculated, 
and hence the values of S and Q. 

Calculation of the Transverse Temperature Difference 
and Potential Difference. 

Before the magnet is excited there will be a certain difference of 
temperature between A and C. Let 0 be this difference, A being at 
a higher temperature than C. On account of this there will be an 

E.M.F., E, acting from A to C in the copper circuit, and an E.M.F., e, 
acting from A to C in the constantan circuit. If M and N are the 
thermoelectric powers of the metal of the plate with respect to copper 
and constantan respectively, there will be the relations : — 



When the magnetic field is excited, the temperature difference 0 is 
altered to some value 0 + SO, and at the same time a transverse potential 
difference is set up. Let this potential difference, measured from A to C, 
be denoted by V. 

Let the new values of E and e be E + <SE and e -f Se. 

There will be the relations : — 



from A and C to the other galvanometer circuit. Simultaneous readings 



E= -M0 
e= -N 0 



( 1 ) 

( 2 ) 



E + SE = V-M (6 + 8$) 
e + 8 e = Y_N (0 + S0) 



(3) 

(P 



Now, by subtraction of (4) from (3), 

(E - e) + (SE - Se) = (N - M)0 + (N - M )S0 
and from (1) and (2), 



E-e = (N-M )6; 



therefore 



SE-8e = (N-M)S0, 



or 




1913-14.] The Hall and Transverse Thermomagnetic Effects. 213 



Now (N — M) is the thermoelectric power of copper with respect to 
constantan, and is known from the results of a special experiment. The 
value of SO can therefore be calculated from the observations <5E and Se c 
Again, by (1) and (2), 

E_M 
e ~N’ 

so that (3) and (4) may be written 

E + SE = V - M(0 + SO) 

(e + $e)x- = Vx?-M(0 + S0), 
e e 

from which 
and hence 

y _e8E-E8« 
e - E 

The transverse potential difference V can thus be determined from the 
observations E, e, <5E, and $e. 



Hall Effect. 

The tubes and jackets were supplied with steam or cold water in order 
to bring the plate to the required temperature. A current of 10 amperes 
was passed through the plate, and the temperatures at E, B, and D were 
measured ; observations being taken also with the current reversed, in order 
to correct for any direct action of the current on the E.M.F.’s at the 
junctions. 

The copper wires at A and C were then connected to one galvanometer 
circuit and the constantan wires at A and C to the other, and readings 
were taken with magnetic field zero and also with known magnetic fields 
in each direction. From these readings the transverse E.M.F. due to the 
magnetic field could be calculated. 

The potential gradient along the axis of the plate was determined by 
connecting the copper wires at E and D to one galvanometer and the 
constantan wires at E and D to the other, and taking readings with both 
directions of the current. 

The value of R was then calculated in accordance with the definition 
given. 

No correction was made for the influence of the Transverse Galvano- 
magnetic Temperature Effect, as, in the case of the metals tested, this 
effect is very small. 



214 



Proceedings of the Royal Society of Edinburgh. [Sess. 



Results. 

Nickel: — Thickness of plate = 0-275 mm. 

The thermomagnetic temperature and potential effects were measured 
in magnetic fields of various strengths and at three temperatures, namely, 
43° C, 61-5° C., and 126° C. 



Temperature of Plate = 43° C. 


Temperature of Plate = 61 *5° C. 


Temperature of Plate = 126° C. 


Magnetic 

Field. 


S x 10". 


Q x 10 4 . 


Magnetic 

Field. 


SxlO 7 . 


Q x 10 4 . 


Magnetic 

Field. 


S x 10 7 . 


Q x 10 4 . 


2,000 


-7T0 


-3P0 








2,900 


-5*55 


- 78-0 


4,200 


-6-80 


-29*5 








4,800 


-515 


-76-5 


6,500 


-6-62 


-27-5 








6,800 


-4-70 


-68*5 


8,300 


-5-78 


-23*5 


8,500 


-5*30 


-34-5 


8,300 


- 4T7 


-58-6 


14,500 

19,100 


-3-50 


- 14-5 








12,000 


-3-01 


1—41*4 


-2*78 


-1P5 








17,350 


— 2T2 


-29-0 


21,900 


- 2-42 


-10-0 


22*600 


— 2-*25 


-14*5 


22,100 


-1*78 


-23*5 








... 


22,800 


- 1-74 


-22-2 



The coefficients S and Q are both negative, and vary greatly with the 
strength of the magnetic field. The numerical value of the coefficients 
decreases as the field strength increases. 

An increase of temperature causes a decrease in the numerical value of 
S, but a very large increase in the numerical value of Q. 



Magnetic 

Field. 


Range of 
Temperature. 


Temperature 
Coefficient of S. 


Temperature 
Coefficient of Q. 


8,500 | 


43° C.-6P5° C. 


- 0-0039 


+ 0-027 


61*5° 0.-126° C. 


- 0-0033 


+ 0-011 


22,000 | 


43° C.-61-5 0 C. 


- 0-0028 


+ 0-026 


61-5° 0.-126° C. 


- 0-0035 


+ 0-009 



Hall Effect . — This was measured in magnetic fields of strength varying 
from 2000 to 22,000 units, and at temperatures of 14° C. and 101° C. 



Temperature of Plate = 14° C. 


Temperature of Plate = 101° C. 


Field. 


R x 10 7 . 


Field. 


R x 10 7 . 


2,050 


-9-10 


2,100 


-12-0 


3,800 


-8-95 


4,060 


-10-9 


6,300 


-8-10 


6,400 


- 10-0 


8,200 


-7T0 


9,500 


- 7-27 


14,300 


-4-50 






18,800 


-3'59 






21,750 


- 3-21 


21*900 


- 3*48 



1913-14.] The Hall and Transverse Thermomagnetic Effects. 215 

The coefficient R is negative and varies with the field strength in 
practically the same way as S and Q. 

Increase of temperature increases the numerical value of R. 

Temperature coefficient of R in field of 6,400 units = +00025. 

1 | 22,000 „ =+ 0 - 0010 . 



Iron. Thickness of plate = 0*51 mm. 

Thermomagnetic Temperature and Potential Effects . — These were 
measured in magnetic fields varying from 2000 to 22,000 units, and at 
temperatures of 48*6° C., 71*5° C., 97 - 9° C., and 129-2° C. 



Temperature of Plate 
= 48-6° C. 


Temperature of Plate 
= 71-5° C. 


Temperature of Plate 
= 97-9° C. 


Temperature of Plate 
= 129-2° C. 


Field. 


S x 10 7 . 


Q > 


<10 4 . 


Field. 


SxlO 7 . 


Q x 10 4 . 


Field. 


S x 10 7 . 


Q x 10 4 . 


Field. 


S x 10 7 . 


Q x 10 4 . 


2,100 


+ 5-75 


+ 


10*0 


2,000 


+ 6*45 


+ 10-8 


2,100 


+ 7-16 


+ 


12*8 


2,000 


+ 6-05 


+ 10-9 


4,000 


+ 5-44 


+ 


10*2 


4,000 


+ 6-27 


+ 9-7 


4,300 


+ 6-24 


+ 


11-7 


4,500 


+ 6-98 


+ 10-1 


6,500 


+ 5-20 


+ 


10-1 


6,000 


+ 6-00 


+ 10-5 


6,300 


+ 6-10 


+ 


11-5 


6,650 


+ 6-31 


+ 10*4 


8,550 


+ 5-47 


+ 


10-6 


8,300 


+ 5-82 


+ 10-4 


9,250 


+ 6*26 


+ 


10-6 


8,200 


+ 6-25 


+ 10-5 


11,300 


+ 5'54 


+ 


10*9 


11,400 


+ 6*08 


+ 10-3 










11,500 


+ 6-21 


+ 10-3 


14,800 


+ 5-48 


+ 


10-6 


14,900 


+ 5-92 


+ 10-8 


16,400 


+ 5-85 


+ 


ii-6 


14,250 


+ 6-12 


+ 9-9 


17,600 


+ 5-26 


+ 


9-9 


17,550 


+ 5*72 


+ 97 


20,300 


+ 5-65 


+ 


10-5 


19,300 


+ 5-70 


+ 9'2 


22,650 


+ 4-88 


+ 


9-1 


22,500 


+ 5-40 


+ 8*7 


23,300 


+ 5*30 


j. 


9-5 


22,100 


+ 5-39 


+ 8*6 



The coefficients S and Q. are both positive ; they decrease slightly as 
the magnetic field is increased. As the field approaches the value 20,000 
units, a more rapid decrease in the values of S and Q is observed. 



Field. 


Range of 
Temperature. 


Temperature 
Coefficient of S. 


Temperature 
Coefficient of Q. 


22,500 1 


48-6° C.-71-5 0 C. 
71-5° C.-97'9° C. 
97-9° C.-129-2 0 C. 


+ 0-0045 
zero 
zero 


- 0-002 
+ 0-005 
- 0-002 



Up to about 70° C. the value of S increases considerably with 
rising temperature, but between 70° C. and 130° C. it remains nearly 
constant. 

The variation of Q is not so simple. As the temperature is 
increased the value of Q at first decreases, then increases, and finally 
decreases again. 



216 Proceedings of the Royal Society of Edinburgh. [Sess. 

Hall Effect . — This was measured in magnetic fields of strengths varying 
from 2000 to 22,000 units, at temperatures of 13-3° C. and 99-8° C. 



Temperature of Plate = 13-3° C. 


Temperature of Plate = 99-8° C. 


Field. 


R x 10 7 . 


Field. 


R x 10 7 . 


2,250 


+ 6-60 


1,950 


4-965 




4,050 


4-8-75 


5,500 


+ 6T0 


6,400 


4-8-83 


8,450 


4-6T7 


9,500 


4-9*00 


15,000 


4-6-26 


14,850 

17,300 


+ 8 95 


19,000 


4-6-06 


+ 8-70 


22,600 


4-5-73 


22,600 


+ 8-01 



The coefficient R is positive ; it decreases with increasing field, very 
slightly at first, but more rapidly as the field approaches 20,000 units. 

Increase of temperature produces a very marked increase in the 
value of R. 

Temperature coefficient of R in field of 6,400 units = +0*0052. 

„ „ „ 22,600 „ =+0*0046. 



Copper. Thickness of plate = 0-063 mm. 

Thermomagnetic Temperature and Potential Effects . — These were 
measured in magnetic fields of three different strengths, and at three 
temperatures, viz. 43*9° C., 70-7° C., and 125’8° C. 



Temperature of Plate 
= 43-9° C. 


Temperature of Plate 
= 70-7° C. 


Temperature of Plate 
= 125-8° C. 


Field. 


S x 10 7 . 


Q x 10 4 . 


Field. 


SxlO 7 . 


Q x 10 4 . 


Field. 


SxlO 7 . 


«C 

X 

I — 1 

© 


7,850 


-2'04 


+ 1-61 


7,900 


-1-75 


+ 1-53 


7,700 


-1-74 


+ 1-48 


13,550 


-2-20 


+ 1-67 


13,650 


- 1-84 


+ 1-53 


13,000 


- 1-80 


+ 1-47 


21,400 


-2-27 


+ 1*69 


21,400 


-1-86 


+ 1-55 


21,150 


-1-74 


+ 1-47 



The effects are of opposite signs, S being negative and Q positive. 
The values of S and Q are only slightly affected by the strength of the 
magnetic field. 

Increase of temperature causes a diminution in the numerical values of 
both S and Q, and the rate of diminution decreases as the temperature rises. 

Temperature coefficient of S in field of 21,000 units for range — 

43 9° C. to 70-7° C.= -0-0068. 
„ „ „ „ 70-7° C. to 125-8° C.= -0 0012. 

„ „ Q „ 43-9° C. to 70-7° C. = - 0-0031. 

70-7° C. to 125-8° C. = -0-0009. 



1913-14.] The Hall and Transverse Therm omagnetic Effects. 217 

Hall Effect . — This was measured in magnetic fields of strengths of about 
8000 and 22,000 units, and at temperatures of 15 6° C. and 99'8° C. 



Temperature of Plate = 15*6° C. 


Temperature of Plate = 99 ‘8° C. 


Field. 


E x 10 7 . 


Field. 


E x 10 7 . 


8,200 


-2-61 


8,000 


-2-00 


22,000 


-2-76 


21,500 


-2-06 



The coefficient R is negative and is but slightly affected by the strength 
of the magnetic field. The numerical value of R decreases very consider- 
ably with increasing temperature. 

Temperature coefficient of R in field of 22,000 units = — 0-0038. 

Zinc. Thickness of plate — 015 mm. 

Thermomag netic Temperature and Potential Effects . — These were 
measured in magnetic fields of three different strengths, and at temperatures 
of 46-4° C., 74-4° C, and 128-3° C. 



Temperature of Plate 
= 46-4° C. 


Temperature of Plate 
= 74-4° C. 


Temperature of Plate 
= 128-3° C. 


Field. 


S x 10 7 . 


Q x 10 4 . 


Field. 


S x 10 7 . 


Q x 10 4 . 


Field. 


SxlO 7 . 


Q x 10 4 . 


7,700 


+ 1-04 


+ 1-24 


7,700 


+ 0-95 


+ 1-35 


7,700 


+ 0-83 


+ 1-30 


13,500 


+ 1-05 


-h 1*26 


13,300 


+ 0-98 


+ 1-34 


13,500 


+ 0-80 


+ P26 


21,100 


+ 1-06 


+ 1-32 


21,200 


+ 0-97 


+ 1-44 


21,400 


+ 0-82 


+ 1-20 



The coefficients S and Q are both positive, and they vary slightly 
with variation of magnetic field. The value of S decreases steadily 
with increasing temperature. The value of Q increases up to a certain 
temperature, beyond which an increase in temperature produces a de- 
crease in Q. 

Temperature coefficient of S in field of 21,000 units for range — 

46*4° C. to 74-4° C. = - 0-0030. 
74-4° C. to 128-3° C.= -0-0030. 
46-4° C. to 74*4° C.= +0-0032. 
74-4° C. to 128-3° C.= -0 0031. 



Q 



218 Proceedings of the Royal Society of Edinburgh. [Sess. 

Hall Effect . — This was measured at temperatures of 15‘9° C. and 
101*5° C. 



Temperature of Plate = 1 5 9° C. 


Temperature of Plate = 101-5° C. 


Field. 


R x 10 7 . 


Field. 


Rx 10 7 . 


7,700 


+ 1-40 


7,800 


+ 0-95 


13,200 


+ 1-41 


13,770 


+ 0-98 


21,300 


+ 1-43 


21,300 


+ 0-99 



The coefficient R is positive, and increases slightly with increasing 
magnetic field, but decreases with increasing temperature. 

Temperature coefficient of R in field of 21,300 units = —0*0037. 

Aluminium. Thickness of plate = 0*25 mm. 

Thermomagnetic Effects . — These were measured at 40° C. 

Coefficient S in field of 22,700 units = — 6*3 x 10 ~ 8 . 

Q „ 22,700 „ 3-9xl0- 5 . 

Hall Effect . — This was measured at 14*5° C. 

Coefficient R in field of 21,600 units = — 1T5 X 10 " 7 . 



Discussion of Results. 

It will be seen from the following table that, although the Hall and 
thermomagnetic temperature effects vary both in magnitude and sign 

R 

from metal to metal, the ratio is for all the metals tested of the same 

k5 

positive sign, and does not vary greatly in magnitude. The ratio is not 
greatly affected by change of temperature, except in the case of nickel. 



Metal. 



Nickel 
Iron . 
Copper 
Zinc . 

Aluminium 



Field. 


Value of Ratio -5 . 

O 


Temperature 
44° C. 


Temperature 
100° C. 


8,500 


1*32 


1-83 


23,000 


1-37 


1-90 


8,000 


1-34 


1-44 


22,000 


1-36 


1-49 


8,000 


1-18 


1-15 


21,000 


109 


1T8 


8,000 


1-19 


1-07 


21,000 


1-20 


1-09 


22,700 


1-83 





1913-14.] The Hall and Transverse Thermomagnetic Effects. 219 

The ratio ^ varies from metal to metal. It is positive for all the 
metals tested except copper. The values are given in the following table : — 

Field strength = 21 ,000. 



Metal. 


at 45° C. 
Jti 


-§at 100° C. 

JLV» 


Nickel 
Iron . . . 

Copper 

Zinc .... 
Aluminium 


+ 3'25 x 10 3 
+ l-39xl0 3 
- 0'68 x 10 3 
+ T07x 10 3 
+ 0-34xl0 3 

1 


+ 6 0 xlO 3 
+ 1T8 x 10 3 
- 0’73 x 10 3 
+ 1*40 x 10 3 



It may he of interest to consider these results in their relation to the 
electron theory. In the development of this theory some difficulty arises 
in explaining the variation of the signs of the transverse effects. Drude * 
in his investigation assumes the existence of positive and negative carriers 
both taking part in the transmission of the heat and electric currents. 
Drude finds the following expressions for the Hall and thermomagnetic 
transverse effects : — 

r t = 

\ x 1 + x 2 ) 

Q = — + °"2^2^/l) 

( T 

® = l2/2)’ 

CCT 

where 

„ „ _d(log »j) 

1 dt ’ 2 W~ ’ 

y 1 = eVj, y 2 = ev 2 , 

cr 1 = e 2 v l n 1 , cr 2 = e 2 v 2 n 2 , a = <r 1 + <x 2 . 

and n 2 are the numbers of positive and negative carriers respectively 
in each unit volume of the metal. 

e = the magnitude of the charge on each carrier. 

and v 2 are the average velocities impressed on the positive and 
negative carriers respectively by unit electric field. 
p and c are constants. 

Now if x 1 and x 2 have the same sign, R and S are both differential effects 
* Ann. d. Phys ., vol. i., 1901. 

+ The expression for R given by Drude has been multiplied by <r in order to make it 
applicable to the coefficient R as defined in this paper. 



220 Proceedings of the Royal Society of Edinburgh. [Sess. 

and may of course vary in sign from metal to metal, but R and S will both 
have the same sign in the same piece of metal. This is quite in accordance 
with experiment. 

In the case of the coefficient Q, it will be seen that a diversity of sign 
can only occur if x x and x 2 have opposite signs, which is not a very likely 
proposition. In any case, there would be no reason to expect any close 
relation between the sign of Q and the sign of R. Experiment shows, 
however, that these coefficients have in general, though not always, the 
same sign. 

R 

Again, in order to account for the fact that the ratio -g has nearly 

the same value for all metals, it must be supposed that one group of 
carriers is of small importance compared with the other. 

It would seem, therefore, that the difference in the signs of the 
transverse effects in different metals must be referred to some cause 
other than the participation of positive as well as of negative carriers 
in the transmission of the current. 

Sir Joseph Thomson * has suggested that the reversal of the Hall 
effect in iron may be due to the fact that the magnetic field close to a 
molecule is in the opposite direction from the magnetic field in the free 
space between molecules. The Hall effect would thus be a differential 
effect, and the reversed sign would be easily accounted for. 

A. W. Smith f has put this to the test of experiment by measuring 
the Hall effect in iron at various temperatures up to 1000° C. No 
reversal of the sign of the Hall effect was observed, although iron loses 
its magnetic properties at a temperature considerably below 1000° C. A 
simple inspection of the values of the Hall effect for different metals 
is sufficient to show that there is no direct relation between the sign 
of the Hall effect and the magnetic properties of the metal, for the 
effect is positive in both iron and zinc, while it is negative in both 
nickel and copper. 

Nevertheless, a differential action such as Thomson has suggested would 
carry us far towards an explanation of the experimental results, if it could 
be supposed to occur in all metals whether magnetic or not. Such a 
differential action would apply with equal force to all the transverse 
effects, and would thus account for the experimental relation between 
R and S. The fact that the relation between Q and R is not so simple 
is not difficult to understand, for in the case of the thermomagnetic effect 
the temperature gradient in the plate sets up a potential gradient along 



* Corpuscular Theory of Matter. 



t Phys. Rev., Jan. 1910. 



1913-14.] The Hall and Transverse Thermomagnetic Effects. 221 



the plate, and this will have an effect on the value of Q. In consequence 
of this, it is not to be expected that the ratio ^ will be so nearly 

constant as | 



On examining the experimental results, it will be seen that there is 
no simple relation between the temperature coefficient of Q and those of 
R and S. This is easily accounted for by the fact, previously pointed out, 
that the potential effect is influenced by causes other than those which 
determine the other two effects. On the other hand, some relation is to 
be expected between the temperature coefficients of R and S. 

On the assumption that only negative carriers need be considered, 
the electron theory leads to the expressions 



R = A 



eXu 



S = B 



eXu 

I^T 



j 



where e = the electronic charge 
A = mean free path, 

u= ^/njean square velocity of electrons, 

«T = K.E. of electron at absolute temperature T due to its linear 
motion. 

A and B are factors depending upon the distribution of the magnetic 
field within the metal. 

Now, if R and S are influenced in the same way by the distribution 

R 

of the magnetic field, the value of is unity, and should be independent 

o 

both of field strength and temperature. There is a rough approximation 
to this in the case of copper and zinc. In the case of iron the value of 
R 

g-, although considerably greater than unity, does not vary greatly with 

variation of either field strength or temperature. 

In the case of nickel, however, a very considerable discrepancy is 
apparent. It is difficult to account for this discrepancy except on the 
assumption that the values of R and S do not depend in quite the same 
way upon the distribution of the magnetic field. This is not inconceivable, 
since in the case of the heat current the electrons are moving with 
velocities which remain constant between two collisions, whereas in the 
case of the electric current the velocities of the electrons are subject to an 
acceleration. 

The galvanomagnetic temperature effect, which has not been considered 
in this paper owing to the difficulty experienced in measuring it in such 



222 



Proceedings of the Royal Society of Edinburgh. [Sess. 

metals as copper, zinc, and aluminium, is of considerable theoretical 
interest. In accordance with the theory of the differential field, the sign 
of this effect should change along with the sign of the Hall effect, whereas 
in accordance with Drude’s statement of the theory it should be of the 
same sign in all metals. Zahn has measured the effect in several metals, 
but it so happens that, owing to the metals used, no definite conclusions 
can be drawn from the results. The author hopes to carry out further 
experiments on this point. 



( Issued separately August 4, 1914.) 



1913-14.] 



Some Factorable Continuants. 



223 



XVI. — Some Factorable Continuants. By W. H. Metzler, Ph.D. 



(MS. received May 15, 1914. Read June 15, 1914.) 



1. In the Transactions of the South African Philosophical Society for 
January 1905, Dr Thomas Muir gives the most general continuant resolvable 
into factors by means of a given set of line-multipliers. He starts with 
the multipliers and determines the continuant resolvable by them. At the 
end of his paper he gives another continuant and its factors, but not the 
line-multipliers, which he says “ is equally interesting in itself and equally 
full of promise as a base for investigation.” Throughout his paper Muir 
is dealing with one of the two determinant factors of order n into 
which every centro-symmetric continuant of order 2 n can be broken up. 
Starting with the larger continuant of which Muir’s is a factor, one of the 
objects of this paper is to determine a set of row and column multipliers 
that will cause the continuant to break up into quadratic factors and 
thence into linear factors. Other and more general types of con- 
tinuants are given which these same multipliers reduce to quadratic 
factors. Another and more convenient way to determine the factors 
of these determinants is obtained in the form of reduction formulas. 
It is also shown how, for the two parts of order n into which the 
larger continuant of order 2n breaks up, the linear factors come out 
by reduction. 

2. The determinant in question is 



T = 



a 



(~n- l)fi 
2rc-l 



!.(/? + 'In - 2) (2rc-2)(/?+l) 

3-2 n 'In - 3 

■ 2.Q8+2rc-3) (2rc-3)Q8 + 2) 

5 - 'In ! 'In - 5 



(2»-2)(/i+l) „ l.(/3 + 2»-2) 
2/4 — 3 3-2 n 



(2m- l)j8 
2n- 1 



a 



2 n 



{a 2 -£ 2 }{a 2 -(/? + 2) 2 } . . . (a 2 -(/3 + 2rc-2) 2 }, 



224 Proceedings of the Royal Society of Edinburgh. [Sess. 



and the multipliers are 



C 2 A -1 + 



k(2n - 4& - 3) 



1) 



C2*+l 



(2 n - 2 k ■ 
k + h-1 

k-l .\h ' (2w - 2k + l){2n — 2A? — 1 ) . . . (2% - 2k + 1 - 2 . h^l) 



(2 n - 4& + 3)(2?i - 4& + 1) . . . (2% - 4& + 3 - 2 . A - 1 'jp . 

V = r ; C2fc+2^-l + 



C 2 & + 



&(22i-4&+l)^ 

( 2 tt - 2 £- l )° 2A:+2 + ‘ * ‘ 

| |^ + 7t ~ 1 (2?t-4A:+l)(2?i-4fe-l). . .(2n-4&+l-2.~fe^l ) 0; ^ + 

lAzl* I* ’ (2n-2fc-l)(2n-2&-3). .. (2»-2&-l -2.1^1) 2 * +21 
(A-l)(2w-4A + 5) 1 



+ (-> 



(2n-2* + l) 
| fc-l 



-R 2&-2 + • • • 

(2?i-4& + 5 + 4 . h 



1)(2 n - A.k + 3)(2w- - 4fc + 5) , 



b»+i 



| k-h-l , \h 

k(2n - 4^ + 3)t, 

■KsSfc-r 

(2 n 



{2u — 4k -f- 3 + 2 . li — 2)p . 

: -&2k-2h + 



(2 n - 2& + 1) 

„ \k 
+ (~) h - 



{2n-2k + l){2n-2k + Z). . . (2?i - 2&+ 1 +2 . h- 1) 



4fc+3+4. fr-l)(2tt-4& + l)(27i-4fr + 3). . . (2ro-4fc + l + 2. ft-2 ) R ^ + 



| ^ (2w-2fc + l)(2w-2& + 3). . . (2?i-2fc + l + 2. fc-1) 

where C* and R, represent the ith column and jth row respectively. 

3. The work of finding these line-multipliers will not be given here, 
though a few words as to the method used may be of interest. A series of 
consecutive non-zero elements along and parallel to the principal diagonal, 
beginning with that in the 2rth row and 2rth column, were written down, 
and the various multipliers for these general rows and columns determined 
under the conditions that when all the operations were completed the result- 
ing determinant was such that all the elements, say below the principal 
diagonal, were zero, except those in the odd places of the line immediately 
below the principal diagonal, in which case the determinant obviously breaks 
up into quadratic factors, each of which is the difference of two squares. 

4. As an illustration take the determinant of order eight 

a 0 ! 

ft + 6 6(0 + 1 



- o 

2(0 + 5) 

-3 

3(0 + 4 ) 
- 1 



5(0 + 2) 



4(0 + 3) 

1 



4(0 + 3) 



3(0 + 4) 

1 " -1 
5(0 + 2) 2(0 + 5) 

a -3 



3 



6(0 + 1 ) 



0 + 6 

-5 



0 



1913-14.] Some Factorable Continuants, 

and perform the operations 



225 



Cj + C 3 + C 5 + c 7 , 

C 2 + C 4 + C 6 + C 8 , 

E 8 + 9E 6 - 5E 4 - 5R 2 , 
R r + E 5 -|E 3 -4E 1 , 



C 3 + f c 5 + fC 7 , C 5 -C 7 , 
C 4 + |C 6 -C S , C 6 - 9C 8 , 

-^G _ f-^4 - > -^4 “ -^2 ’ 

R 5 - f R 3 + tRj. » R 3 -Ri, 



and we have 

a f3 

(3 a 108 + 1) 

0 a f(/3 + 2) 

!(£ + 2)' a 4(0+3) 

0 a M±l) 

-K/8 + 4) a 

0 a 

- 5 

- 5(/3 + 6) a 



= (a 2 - /3 2 )(a 2 - 0 + 2 2 )(a 2 ~/3 + 4 2 )(a 2 - /3 + 6 2 ) 
= (<2 + + (3 + 2)(a + (3 + 4)(a + (3 + 6) 

(a-0)(a-0-2)(a-0-4)(a-0-6). 



5. Other and more general types of continuants than T tt given in art. 2, 
whose quadratic factors are brought out by the same set of line-multipliers, 
are the following : 



(2 n-W 
2 n - 1 

a + (2n — 2)y b ( 2»-2)(q + y ) 

3-2 n 2n - 3 

2{^+ (2w - 3)8} a (2w - 3)( 0 + 28) 
5-2 n 2n- 5 



(2n-2XP+_S) fi + ( 2n-2)S 

2n - 3 3-2 n 

(2n — l)a 
274-1 



2w 



= {a&-a0}{a5-(a + 2y)(0 + 2S)} . . . - (a + 2» - 2. y)(fi + 2n - 2 . 8)}, 

VOL. XXXIV. 15 



226 



Proceedings of the Poyal Society of Edinburgh. [Sess. 



and 



T = 



(2n - l)a(/5 + 2n-2) 
2 n - l 



y(S + 2n - 2) , (2n - 2) { S(y + 2n - 3) + y } 

3 - 2n 2w - 3 



2{/3(a+2w-3) + a} 
5 - 2n 



(2n - 3){a(/S + 2n - 4) + 2/3} 
2n-5 



(2n - 2){a(/3 + 2n — 3) + (3} 
2n-3 



/3( a + 2 n - 2) 

3 -2n 



(2n-l)8 (y+2w-2) & 

2ra~ 1 



= {ab - a(P + 2 n - 2)8(y + 2n - 2)} - (a . (3 + 2n - 4 + 20)(8 . y + 2n - 4 + 2y) j . . . 

{ah - (3(a + 2 n- 2)y(8 + 2w - 2)}. 



If in T 6 we change the sign of /3 and S, which is equivalent to changing 
the signs of the elements below the principal diagonal, the signs between 
the terms of the binomial factors would be plus instead of minus. 

6. If in T & we put : 

(1) b — a, a = f3, and y = S — 1, it reduces to T a ; 

(2) y = ^ = 0, all the factors are alike and we have 

T b = (ab -a f3) n , 

or if, in addition, b = a and a = 3, 

T,=K-^ r . 



(3) y — — a and S = — (3, two factors become alike and 

T & = (ab - a/3) 2 (ab - 9 af3) . . . (ab -2 n- 3 2 ‘af3 ) ; 

(4) a = y — = y and b = a, then 



T„=(<j2_12)( a 2_ 3 2) . _ . («2_2n-l 2 ). 



This, as far as the factors are concerned, is equivalent to putting 
a = f3 = y = S = 1, 

or « = y = and /3 = S = k, where k is any number, 

or p — a-2n—l, y = S= —2. 
or i3 = a = 2n—l,y = S——l; 



Some Factorable Continuants. 



227 



1913-14.] 



(5) /3 = — a = 2n— 1, y = — 8 = 2, then 

T, = (a 2 +l 2 )(a 2 + 3 2 ) # . . («2 + 2 ^Tl 2 ) j 
which is Elliott’s form.* 

(6) a = /3 = 0, y = S = 1 , and b = a, then 

T & = a 2 (a 2 — 2 2 )(a 2 - 4 2 ) . . . (a* - 2n^2 2 ) ; 

(7) a — 6 = 1, y — S = i, and b = a, then 

T & = (a 2 -l 2 )(a 2 -2 2 ) . . . (a 2 -ft 2 ); 

(8) a = — ft = 1, y = — S = ^, and b = a, then 

T & = (a 2 + l 2 )(a 2 + 2 2 ) . . . (a 2 + ft 2 ). 

7. If in T c we put : 

(1) S = a, y = /3, and b = a, then 

T ={a 2 - a 2 (/3 +2 ft - 2) 2 } {a 2 - (a . (3 + 2n - 4 + 2/1) 2 } . . . {a 2 - £ 2 (a + 2 tz - 2) 2 } ; 

(2) S = y = /3 = a and b = a, then 

T c = {a 1 - a 2 (a + 2ft - 2) 2 }’ 1 ; 

(3) S = y = /3 = a = b = a, then 

T c = a 2w (2ft + a - 1 ) w (3 - a - 2 n) n , 
or if a -f 2 tz — 2 = a;, then 

T c = (l 2 -a 2 ) B (a;-2ft-2) B . 

If a = 1, then 

T c =2*{n(l-ft)}»; 

(4) <S = y = /3 = a = l, b = a = x(2n — 1), then 

T c = (2ft - l) 2?1 (x 2 - l 2 ) w . 

If = T c = 0. 



8. It will be observed that in (2) of articles 6 and 7 we have a 
determinant of the 2r&th order expressed as the Tith power of a determinant 
of the second order. 

From (4) of article 7 it is seen that the determinant 

x 1 

1 2 n - 2 

3 — 2 n 2?i — 3 

2 2n - 3 
5 - 2ft X 2ft - 5 

- (* 2 -iy. 



i 

X ■ 

3-2 ft 

1 x 



* Proceedings of London Mathematical Society, vol. xxxiii. p. 229. 



228 



Proceedings of the Koyal Society of Edinburgh. [Sess. 

9. There is another and simpler way of getting the factors of these 
continuants. For instance, if in T a we add to every odd column the sum 
of all the odd columns which follow it, and add to every even column the 
sum of all the even columns which follow it, then subtract from every row 
the second row above it, the determinant breaks up into (a 2 — /3 2 ) and a 
determinant of order (2 n — 2), which on interchanging the denominators of 
conjugate elements is a determinant of exactly the same form with n one 
less and /3 two more. Thus, if T a be represented by f 2n (a, /3), then 

/*»(«, /?) = (« 2 -/3 2 )/ 2 n- 2 («, £ + 2). 

In precisely a similar manner, if T & is represented by / 2n (a&, a/3), then 
f 2n (ab, a/3) = (ab - a/3)/ 2w _ 2 (a&, a + 2y . /? + 23), 
and if T c is represented by f 2n (ab, a/3, yS), then 

fojcib, a/5, yS) = {ab - a(/5 + 2 n- 2)8(y + 2n - 2 )}f 2n , 2 (ab, a/3 + 2/3, yS + 2y). 

10. It is easily seen that if T ft is represented by f n (a) . F^a), then 

fn( a ) = (a+2n- l) ./ n _!( - a) = (a - 2 n- l)(a - 2n - 3) ./„_ 2 ( a) 

and 

F n (a) = (a - 2n - 1) . F, t ( - a) = (a - 2 n- l)(a + 2n - 3) . F M _ 2 (a), 

which shows that the signs between the terms of the factors are alternately 
positive and negative for f n (a), and negative and positive for F n (a). 

The operations which show this are the following : — 

(1) Add all the other columns to the first. 

(2) Add to every column after the first the second column following it. 

(3) Subtract from each row the second row above it. 

(4) Subtract the first row from the second. 

(5) Interchange the denominators of conjugate elements in the reduced 
determinant. 

11. If in T & we put b — a, a = (3, and S = y, then it breaks up into factors 
which we may represent by f n (a, a, y) and F n (a, a, y), where f n {a, a, y) is 
the sum of two terms, and F n (a, a, y) the difference of the same two terms. 

Using the same set of operations, it is seen that 

/»(«> a > y) = (« + <*)/„_!(«, a + 2y, y) 

and 

F n (a, a, y) = (a- a)F n _j(a, a + 2y, y). 

That is, the linear factors of T & with the positive sign between the terms 
all belong to f n (a, a, y), and those with the negative sign all belong to 
F «(«> y). 



Some Factorable Continuants. 



229 



1913 - 14 .] 



Similarly, if in T c we put b = a, S = a, and y = b, and if 









Us 

ii 

o 

£—4 


a, a /3) . F n (a, 


a/3), 




then 


















i(a, 


ii 

f 


[a + a{(3 + 2 n - 


- 2)/ n _i(a, 


a/3 + 2/J)} 


and 
















F, 


iO, 


aj8) = ■ 


[a - a{/3 + '2n - 


- 2)F n _ 1 (a. 


,<*,8 + 2/3)} 



Syracuse University, 
28 th April 1914. 



{Issued separately September 3, 1914.) 



230 



Proceedings of the Royal Society of Edinburgh. [Sess. 



XVII. — The Analytical Study of the Mechanism of Writing. 

By James Drever, M.A., B.Sc. Communicated by Dr Alexander 
Morgan. 

(MS. received March 16, 1914. Read June 1 , 1914.) 

In the new and rapidly developing experimental science known as Ex- 
perimented Padagogik ” in Germany, “ Pedagogie experimental ” in 
France, and “ Experimental Pedagogy ” or “ Experimental Education” in 
this country and in America, two well-marked and not entirely consistent 
tendencies have been hitherto manifest. On the one hand, there has been 
a tendency, more particularly in Germany, to develop the work in the 
new field on the lines of experimental psychology, and to employ almost 
exclusively the apparatus and methods of that science. On the other hand, 
there has been a tendency, to a very marked extent in this country and in 
America, to endeavour to carry on experimental work entirely without the 
aid of exact and elaborate apparatus, eschewing, even regarding as “ tabu,” 
the methods of the psychological laboratory. Both tendencies are perhaps 
more or less inevitable, and both to a certain extent may be said to have 
been justified by results. Nevertheless, there are certain obvious dangers 
and defects inherent in both, and the whole situation is itself dangerous 
for the new science. 

If we commit ourselves too exclusively to the employment of psycho- 
logical apparatus and the method of the psychological laboratory, there 
is danger of our experimental education becoming merely a branch of 
experimental psychology, which might involve in the first place the 
neglect of certain fields of study, in which such methods and apparatus are 
quite inapplicable, and, in the second place, a dangerous warping of our 
attitude, aim, and evaluation, consequent upon our psychological view- 
point and our restricted field. If, again, we endeavour to carry on our 
experimental work as far as possible without the use of exact and elaborate 
apparatus, no objection can be made to the thing in itself, but the tempta- 
tion is strong to avoid such detailed and fine analytical work as demands 
the use of precise measuring apparatus, and more or less elaborate recording 
apparatus, which in the long run is almost bound to lead to our science 
becoming exceedingly unscientific, by our contenting ourselves with experi- 
mental investigations of the kind that any teacher can carry out in 
any schoolroom, and then deluding ourselves with the idea that elaborate 
and complex statistical treatment of our results will give them scientific 



1913-14.] Analytical Study of the Mechanism of Writing. 231 

validity. Worst o£ all is the antagonism between the two groups of 
workers in the same field, which is all the more dangerous because the one 
group is mainly composed of psychologists, who know little of the practical 
work of education, and rather look down upon the practical teacher, and 
the other group of practical teachers, who have merely a superficial 
acquaintance with laboratory psychology, and distrust the psychologist. 

This condition of unstable equilibrium, if it can be so described, has 
characterised the early stages in the development of other experimental 
sciences in the past, notably of experimental psychology itself. The con- 
dition will pass, but only when the new science comes to its own in a 
developed laboratory equipment, and a developed technique, which are 
peculiar to itself and not merely borrowed from another science. It is 
obvious that experimental pedagogy must always owe a considerable debt 
to experimental psychology, and also that a great deal of good work may 
be done with the simplest apparatus. But there are certain fundamental 
problems of the school, and of life from the school point of view, all 
analytic problems demanding accurate analytical methods, which must be 
entirely ignored or only superficially noticed, if we confine ourselves to 
either or both of these lines of approach. It would seem, therefore, that 
some of the most interesting, and, if not the most important and practically 
valuable, at any rate most significant work in the new field is that which 
undertakes the analytical study, under laboratory conditions and by means 
of laboratory apparatus, of complex processes characteristic of the work of 
the school, from the teacher’s rather than the psychologist’s point of view. 

Such complex processes as reading, writing, and reckoning, either as 
acquired ££ dexterities ” or in the acquiring, may be cited as illustrating the 
field for analytical investigation offered by the school. To the extent that 
such processes are fundamental in school work, their investigation should 
logically occupy a central position in the new experimental science. Con- 
siderable progress has already been made, chiefly in Germany and America, 
in the analytical study of the reading process. The main purpose of the 
present paper is to indicate how a similar study may be made of the 
writing process. This purpose will be best achieved by describing some 
pieces of apparatus which have been devised with a view to the analysis of 
various elements in the mechanism of writing; for the analysis of the 
various factors involved in writing is obviously the first step towards its 
scientific study. The three pieces of apparatus described are all intended 
to isolate elements in the manual mechanism, and they all yield graphic 
records which may be examined at our leisure and compared with the 
actual writing itself. 



232 



Proceedings of the Royal Society of Edinburgh. [Sess. 



I. Hand Movement Apparatus. 

The chief movements made in writing are those of the forearm, of the 
hand, and of the fingers. Of these the only movements presenting any 
difficulty for analysis are those of the fingers, and the finger movements 
are at the same time the most interesting. The isolation of the finger 
movements can be obtained by a process of elimination. In the actual 
writing we have the resultant of all the movements. The hand movement 
is the resultant of all the movements except those of the fingers. Hence, 
if we can trace the hand movement, the difference between this and the 
writing will give us the part played by the finger movement. 

Professor Charles H. Judd has devised and described an apparatus for 
tracing the hand movement during writing ( Genetic Psychology for 
Teachers, New York, 1907). Our apparatus is an improved form of this. 
In Judd’s apparatus a broad strip of metal, bent so as to grip the fifth 
metacarpal bone of the right hand, is bent back a second time on its upper 
surface, so as to hold a wooden pin, to which a tracing arrangement is 
attached by a short metal bar with hinges at each end, allowing free move- 
ment in the plane of the wooden pin and the writing or tracing style. The 
tracing style is cylindrical in shape and brought to a rounded point with 
slits so as to hold ink like a pen point, while it moves freely in a longi- 
tudinal direction through a range of about 1J inches within a light frame. 
The point is kept resting on the paper by gravity alone, and the longi- 
tudinal play is intended to allow for different inclinations of the back of 
the hand to the plane of the paper in different individuals and at different 
points in the writing. 

Judd’s apparatus is defective in several respects. In the first place, the 
position of the tracing arrangement is itself very awkward, since its plane 
is almost parallel to the back of the hand, and in writing it seems to drag 
along the surface of the paper, sometimes interfering considerably with the 
movement of the hand, and always distracting the attention of the writer. 
In the second place, the joints are not sufficiently rigid and the free move- 
ment at the joints intensifies the dragging and distracting behaviour of the 
tracing style, while it also allows the hand to move without the tracing 
point moving. In the third place — and this is the chief defect — gravity 
cannot be relied upon to keep the point constantly on the surface of the 
paper, especially where there are sudden and rapid changes in the inclina- 
tion to the paper of the back of the hand. 

In order to remedy these defects and get an apparatus on which we can 
rely for a true record of the hand movement, it is necessary to attach the 



1913-14.] Analytical Study of the Mechanism of Writing. 233 

tracing arrangement differently to the metal strip, to keep the writing 
point against the surface of the paper by means of a spring, and to prevent 
such movement of the whole tracing arrangement as will tend to cause it 
either to fail to respond to any movement of the hand, or to interfere with 
the attention of the writer or his free hand movement. In the apparatus 
shown (fig. 1) these objects are secured by attaching a metal pin tangen- 
tially to the metal strip where it curves over on to the back of the hand, 
and fitting the tracing arrangement to a tube which passes over this pin 
and is movable along the pin, being fastened by a screw in any position 
that may be necessary for adjustment. All the joints are arranged for 




adjustment and not for free movement. Finally, by means of a spiral 
spring the tracing point after adjustment is kept in contact with the paper. 
The trace itself is given by a capillary glass tracing tube or by a lead 
pencil, the holder for which occupies the place of the tracing style in 
Judd’s apparatus. 

As an indication of the kind of work that may be done with this 
apparatus, some tracings are shown (fig. 2), but the results hitherto obtained 
may also be briefly summarised. 

1. Normally, in careful adult writing, and more especially in pen writing, 
the finer movements in the formation of the letters are due to the fingers. 
As the writing is increased in speed, the hand may take over a larger and 
larger share of the movement, until with very rapid writing the movements 
are sometimes nearly all hand movements. 

2. The main movement of the hand in writing is alternately a rotation 
about an axis in the wrist and about an axis in the elbow with careful 



234 



Proceedings of the Royal Society of Edinburgh. [Sess. 



writing, but as the writing increases in speed the rotation about the wrist 
axis tends to disappear. 

3. In the writing of children the part played by finger movement 
is very variable. In general, hand movement predominates even in 

oCiXtbu A w. 

iO+uJ&r- 








the formation of the letters, but this must not be regarded as a 
universal principle. 

II. Grip Pressure Apparatus. 

So far as the writer knows, no one has hitherto attempted to obtain a 
record of the pressure of grip in writing. The problem undoubtedly 
presents considerable difficulties, but is a very interesting one. The 
apparatus shown (fig. 3), which would therefore appear to be the first 
attempt to get such a record, has several more or less obvious defects, but 



1913-14.] Analytical Study of the Mechanism of Writing. 235 

may be regarded as indicating the general lines upon which any such 
apparatus must be constructed. The essential part of the apparatus is 
the arrangement for receiving the grip in such a way as to enable us to 
record its pressure. This is constructed of rubber and is double walled. 
In its construction two teats are used, a large and a small. These are 
placed one inside the other, the space between their walls being filled with 
mercury and sealed. Finally, a narrow glass tube is passed into the inner 
space, and that too is filled with mercury until the mercury stands about 
two inches up the tube. 

To begin with, a single teat was used, but it was found that, immediately 
under the fingers, with a moderately firm pressure, all the mercury was 
expelled, and the rubber sides pressed together. Consequently it was 
impossible to record the full pressure with this arrangement. This defect 
is remedied by the double teat, arrangement with the sealed space between 




Fig. 3. 



the walls. The record of grip pressure is obtained in the usual way by 
connecting the upper end of the glass tube, which projects above the metal 
holding tube, by means of rubber tubing to a recording tambour. 

The most serious defect of this apparatus is its weight, and this is 
largely due to the use of mercury. It might be possible to replace the 
mercury with a lighter liquid, if one could be obtained which neither 
affected the rubber nor evaporated to any great extent from the inner 
space. It is impossible to use merely an air space between the teats, since 
this makes the holding part of the apparatus much too soft and introduces 
thereby a very disturbing factor. 

III. Point Pressure Apparatus. 

The pressure on the writing point itself has already received a con- 
siderable amount of attention, and has been made the basis for several 
interesting discussions, bearing not only on the psychology of writing, but 
also on the study of defective and feeble-minded children, and of the effects 
of drugs like alcohol on the motor co-ordinations in writing. 

Hitherto the apparatus employed to record what is called par excellence 
writing pressure has in every case recorded the pressure on the writing 
surface rather than on the writing point. Kraepelin employed what he 
called a “ Schriftwage,” which consisted of a plate supported by springs 



236 



Proceedings of the Boyal Society of Edinburgh. [Sess. 



and mechanically connected to a lever for recording on a smoked surface. 
The paper was placed on the pressure plate and the pressure in writing 
on the paper was recorded by the recording lever. Meumann similarly 
employed a pressure plate, but supported it on an air cushion pneumatically 
connected with a recording tambour. The chief defect of any such arrange- 
ment, apart from the complications introduced into the writing process 
itself, is that variations in pressure on the writing plate may be due to 
variations which have no necessary connection with the writing itself, but 
are the result of more or less accidental changes in the position of the 
hand or wrist relatively to the plate. 

The original form of the apparatus shown (fig. 4), which has now been 
modified in some minor respects, was first described by the writer in the 
Journal of Experimental Pedagogy , March 5, 1913. The essential feature 
of the apparatus is that it records the pressure upon the writing point 




Fig. 4. 



itself by receiving the pressure of the top end of the writing instrument 
on a receiving tambour. To this a holding tube is attached into which 
either pencil or pen is slipped. By means of a guiding tube, which serves 
as a holder, the pressure is kept normal to the surface of the tambour. 
In order to lessen friction, as well as to prevent side movements of the pen 
or pencil, a ring — or sometimes two — is placed inside the guiding tube, and 
this just allows the pen or pencil to move freely up and down. By 
connecting the receiving tambour with a recording tambour we get the 
record of point pressure. It is not yet certain whether a light spiral spring 
inside the receiving tambour, in such position that the writing instrument 
presses against it, is an advantage or not. 

For the two pressure recording instruments the names “Grip Pressure 
Cheirograph ” and “ Point Pressure Cheirograph ” might be suggested. 
Both of them might be found serviceable, not merely in the study of writing 
pressure for the purposes of the science of experimental pedagogy, but in 
the science and practice of medicine for the diagnosis of defects in motor 
co-ordination ; as we have indicated, writing pressure, that is point pressure, 
has already been studied to some extent from this point of view. The 
study of grip pressure might also be expected to throw some light on 
writers’ cramp. 



1913-14.] Analytical Study of the Mechanism of Writing. 237 



IV. Results of Study of Writing Pressure. 

Traces obtained with the two pieces of pressure apparatus are shown 
(fig. 5). At the same time it might be well to indicate some of the more 
important results obtained in the investigation of writing pressure. 









VnCTUlTT' 




Fig. 5. 



I. to III. Point pressure tracings from children. Time record in seconds by Jacquet Chronograph. 

l a. Child of six. Words “ The cow gives us milk. ” 

lb. Child of six (first attempt at script). Words “ A man can.” 

l c. Child of six (printing). Words “ A man can run.” 

Ila. Pencil writing, and II&. Pen writing of child of eight. Words “ Moray House School,” written twice in 
each case. 

III. Child of eleven. Pencil writing. Words “ Moray House School,” written twice. 

IV. and V. Point pressure tracings from adults. Time record in J secs, by vibrating spring. 

IVa. Pencil writing, ordinary rate. Words “ Moray House School,” written twice. 

IV&. Pencil writing by same subject, maximum rate. Words “ Moray House School,” written four times. 

V. Pen writing, slow and fast. Words “ Moray House School, written once slow and twice fast. 

VI. and VII. Grip pressure tracings from adults and child of eleven. Time records for adults in i secs, and for 
child in secs. 

Via. Adult pencil writing. Words “ Moray House School.” 

VI6. Adult pen writing. Words “ Moray House School Moray.” 

VII. Child’s pencil writing. Words “Moray House School ” twice, slow and fast. 



The most interesting results are probably those indicative of the 
differences between adult writing and child writing. The grip pressure of 
the adult nearly always shows a rhythmical rise and fall of pressure, which 
is almost as regular in the tracing as the vibrations in the tracing of a 



238 



Proceedings of the Royal Society of Edinburgh. [Sess. 



tuning fork, although with increased speed of writing the amplitude of the 
pressure changes sensibly diminishes. The rhythm is also shown in 
children’s writing from about the age of ten, but the irregularities are very 
marked. It is difficult to get any reliable results with our grip pressure 
apparatus at an earlier age. Analogous phenomena appear in the case 
of point pressure. The point pressure trace of adult writing shows a 
characteristic “ rippled ” top on each wave of pressure, indicating more or 
less rhythmical increase and diminution of pressure. In the child’s writing 
this characteristic is entirely absent before the age of about eleven, and we 
have for our pressure trace either a more or less continuous line, or a line 
that is simply “ crooked,” without any regularity in its crookedness. These 
phenomena are probably in the main phenomena of co-ordination, but they 
also have a psychological interest, as we shall see presently. 

A second characteristic difference between adult and child writing may 
be regarded as due partly also to co-ordination phenomena and partly to 
psychical phenomena. It is well known that the practised reader does not 
recognise the several letters of a word individually, nor does he speak them 
individually, in reading a word, but reads the word, as it were, with a single 
total impulse, either of recognition or of speech. Similarly, the adult writer 
writes a word, not with a separate impulse for each letter, but with a single 
impulse for the whole word. In learning to write, however, the child 
learns first to draw the shapes of the letters, and there is a separate impulse 
for each stroke or letter or group of letters, according to the drawing unit 
with which the child is dealing, and this gradually changes from the stroke 
to the letter, from the letter to the group of letters, from the group of 
letters to the whole word, as the child progresses. These differences are 
well indicated in the point pressure traces. The adult trace shows at once 
that each word is written as a whole. The child, learning to write, shows 
equally unmistakably the units for which there is a single drawing 
impulse. 

Even when the child is taught from the beginning to write continuously, 
the traces can still be easily distinguished by the lack of rhythmical 
pressure variations in the child’s trace. This difference, although in the 
main a phenomenon of co-ordination, is at the same time indicative of the 
nature of the psychical impulse that guides the writing. It is due in part 
to the fact that writing is a form of language, while drawing is not. The. 
rhythm is present because it is the word that is before consciousness, not 
the shape or figure to be drawn. 

Moreover, the language unit is the sentence, not the word, and this 
is generally clearly shown both in speech and in reading. Are there any 



1913-14.] Analytical Study of the Mechanism of Writing. 239 



traces of this in writing ? There are to some extent. In adult writing we 
can often mark off the phrases, at any rate, by the subordination of the 
individual pressures for each word to a single maximum pressure on some 
part, usually the end, of the phrase. While the child is drawing and not 
writing we naturally look in vain for any such characteristic. It must 
be noted, however, that the writing of clerks, whom we may consider 
professional writers, tends to lose this last language mark and tends to 
show an approximately uniform pressure. 

x 







1 



JJ 



\AA/VVV\A/V\/VV 




n 



-jx 



m 






HZ 



— 1/ ry ^— ' 1 




a 


\_ 




5 




Ld 


v — f 


i 



JUt 






ijv ““1 



Fig. 6. 



I. “ Masculine ” type. 

II. “ Feminine ” type. 

III. “Mechanical ” or “ Clerical” type. 



IV. Right-hand writing, and 

V. Left-hand writing without practice by 
same subject. 



Previous workers have sought to distinguish, on the basis of point 
pressure traces, different types of writing and writers (fig. 6). As an 
introduction to any such attempt, it must be stated emphatically that the 
point pressure trace is as characteristic of an individual as] his hand of 
writing or his signature, and even in left-handed writing, without practice 
with the left hand, individual characteristics reveal themselves in the 
pressure trace. Nevertheless, it does seem as if there were distinct types of 
writer. Two adult types have been generally distinguished by previous 
investigators. The one tends to show a single maximum of pressure for 
each word or phrase written as a whole, and tends to increase writing 
pressure with increased speed of writing ; the other tends to show several 




240 Proceedings of the Royal Society of Edinburgh. [Sess. 

maxima of pressure in the word or phrase, or to write with an approxi- 
mately uniform pressure, as in the case of clerk’s writing already cited, and 
also tends to show decrease of pressure with increased speed of writing. 
The first has been called the “ masculine ” type, the second the “ feminine.” 
It seems desirable, however, to distinguish the two varieties appearing 
under the second type, and to recognise three types. The “ clerk ” type is 
quite as marked as either of the others, and is quite as distinct from the 
“ feminine ” as the “ feminine ” from the “ masculine.” Another characteristic 
mark of this third or “ clerk ” type is that the writing speed is normally 
very near the maximum. When such writers are asked to increase their 
speed, they may do so to a slight extent, but often all that happens is a 
breaking down of the uniformity of pressure ordinarily shown without any 
significant increase of speed, and sometimes the speed actually decreases 
as an accompaniment of this breakdown of pressure uniformity, while the 
subject thinks he is writing faster than before. A better name for this 
“ clerk ” type, and more descriptive of its chief characteristics, might be 
“ mechanical ” type. 

There seems little reason to doubt that a considerable development of 
our knowledge of the writing process will take place along the lines of 
investigation indicated in this paper. We might even look forward to the 
founding of a real science of graphology. At all events, many points of 
interest to the teacher, and some of interest to the nerve and brain 
specialist, the alienist, or the general physician must be revealed. 



(Issued separately September 3 , 1914 .) 



1913-14.] Abnormal Echinoids in the Royal Scottish Museum. 241 



XVIII.— Abnormal Echinoids in the Collection of the Royal 
Scottish Museum. By James Ritchie, M.A., D.Sc., Royal 
Scottish Museum ; and James A. Todd, M.A., B.Sc. Communi- 
cated by William Eagle Clarke. (With a Plate.) 

(MS. received May 16, 1914. Read June 1, 1914.) 

CONTENTS. 

PAGE 

I. Introductory Notes on Regulation, Duplication op Parts, Relation op 



Ocular Plates to Coronal Growth, and Condition op Specimens . 241 

II. Examples op Incomplete Development ..... 243 

(i) Amblypneustes ovum. 

(ii) Echinus esculentus. 

III. Total Variation prom Five to Six-rayed Form — Echinus esculentus . 247 

IV. Explanation op Plate ........ 252 



I. 

» 

“ Echini are a particularly good group in which to study questions of 
variation, because here variations can usually be expressed in very 
definite terms of numerical or other equally positive character.” * On 
this account, and because, in spite of much description, the variants liable 
to occur in sea urchins have not yet been exhausted, the three specimens 
described below are recorded. Each of these exhibits a pronounced 
abnormality in the major symmetries. Two of them resemble another 
abnormal echinoid in the same collections, already discussed in Proc. Zool. 
Soc ., f in lacking part of a definite ambulacrum ; but the means by which 
the tests have accommodated themselves to changed conditions of growth 
differ markedly in each of the three cases. The third specimen exhibits, in 
place of the normal five-radiate arrangement, almost perfect hexamery — 
a type of abnormality very different from that of the first two specimens. 
For in these the distortion is due to incomplete development caused by 
interference with the processes of growth, while there the hexamery is a 
fundamental change in symmetry, is congenital in origin, and probably 
represents the type of variation known as duplication of parts. 

* R. T. Jackson, “ Phvlogeny of the Echini, with a Revision of Palaeozoic Species, 5 ’ in 
Mem. Boston Soc. Nat. Hist., vol. vii., 1912, p. 51. 

t Ritchie and MTntosh, Proc. Zool. Soc., 1908, p. 646. 

VOL. XXXIV. 



16 



242 



Proceedings of the Royal Society of Edinburgh. [Sess. 

Before proceeding to the description of these specimens, we would draw 
attention to a few facts of more general interest. 

I. Regulation. — It is clear that where so large an area as an ambul- 
acrum or inter-ambulacrum ceases to grow, after temporary development, 
much rearrangement in plates is necessary in order that the potential gulf 
in the test should be spanned. Two distinct modes of regulation occur. 
In the first place, the remaining plates in the neighbourhood of the 
abnormality may themselves wholly compensate for the deficiency by 
abnormal development in length and breadth. Such is the case in the 
Echinus esculentus already referred to, where, an ambulacrum only having 
dropped out, the two inter-ambulacral series of areas 4 and 5 have, by orderly 
increase, shared in filling in the space ; * or in Philippi’s case of Echinus 
melo ,*j* where the place of an ambulacrum with its associated inter-ambul- 
acral series ( i.e . a ray) is taken by a single inter-ambulacral series from each 
of areas 1 and 5. 

Or, in the second place, orderly growth of normal series of plates may 
be replaced or supplemented by the addition of abnormal plates varying 
much in shape and size. These are sometimes arranged with an approach 
to bilateral symmetry, as in inter-ambulacral areas 2 and 3 of the Ambly- 
pneustes described by Hawkins, J and as in the Amblypneustes described 
below (text-fig. 1), or they may form an irregular medley, as in the 
specimen of Echinus esculentus here described (Plate, fig. 1). 

It seems to be a general rule, however, that neither of these modes of 
regulation altogether compensates for the primary disturbance, for in every 
case growth seems to have been retarded, and the abnormal area is indicated 
by a depression in the test and occasionally by a marked distortion of the 
apical area from its normal position. 

II. Duplication of Parts. — Various stages of the phenomenon of duplica- 
tion have been described in Echinoids (see p. 250). These have represented 
duplicity only in partial degree, but it is possible that the hexamerous 
Echinus described below exhibits almost perfect duplication of both 
ambulacral and inter-ambulacral areas, and so completes the series of 
duplication stages. 

III. Ocular Plates and Coronal Growth. — It is generally held that the 
growth of new plates in ambulacral and inter-ambulacral series proceeds 
from the oculars. The case is stated strongly by Lambert. § 

* Proc. Zool. Soc ., 1908, p. 646. 

+ Archiv f. Naturg ., iii. p. 241, pi. 

f Proc. Zool. Soc., 1909, text-fig. 227. 

§ Lambert, “Note sur un cas de monstrosite de l’apex chez YEchinocorys vulgaris ” 
Bull. Soc. Yonne , 1890, xliv. 



1 9 13-1 4.] Abnormal Echinoids in the Royal Scottish Museum. 243 

“ Les centres vita ax de l’apex sont dans les ocellaires et non dans les 
genitales, et c’est seulement a l’abri et au contact des ocellaires que se 
torment les nouvelles annles ambulacraires ou que naissent les anules inter- 
radiales.” Again Jackson, in his monumental and masterly monograph,* 
says : “ The ocular plates seem to exert a controlling influence in the building 
up of the corona, as below and in immediate contact with the oculars 
originate the coronal plates both ambulacral and inter-ambulacral ” (p. 35). 
And again : “ If this is true, then the loss of an ocular would cause a failure 
to develop of the plates that normally went with it ; also an abnormal 
position of an ocular should cause an abnormal distribution of the associ- 
ated coronal plates ” (p. 36). 

The present abnormal specimens offer two comments on these statements. 
In the hexamerous Echinus esculentus, the ocular of the posterior 
ambulacrum (say VI.) is wholly subtended by genital 5, which extends 
some distance on both sides of it (Plate, fig. 2, and text-fig. 3). Yet 
this derangement of the ocular as regards its relations with the genital 
plates has not affected the growth of the coronal plates, which spring in 
normal manner from the sides of the ocular. On the other hand, in each 
of the deficient Echinus esculentus and Amblypneustes one ocular plate is 
awanting, and nevertheless coronal plates have still continued to be formed 
all along the exposed margins of the genitals (text-figs. 1 and 2). These 
plates are very irregular in shape and do not belong to the normal coronal 
series, but are sufficient to show that the growth areas are not associated 
in any essential way with the ocular plates. 

IV. Preservation of Specimens. — It may be worth drawing attention to 
the fact that the specimens, though dried, had not been “ cleaned.” In two 
cases, therefore, the sex was able to be distinguished from the shrivelled 
reproductive organs, and in one case examination of the cruder internal 
structures was made. 

II. Examples of Incomplete Development. 

(i) Amblypneustes ovum (Lamarck). 

The specimen is a male example of Amblypneustes ovum collected at 
the National Park, Wilson’s Promontory, Victoria, N.S.W., in October 1910, 
and presented to the Museum among a number of others by Lord Carmichael 
of Skirling. 

The test, when examined, was dry and denuded of spines. Its maximum 

* Jackson, R. T., “The Phytogeny of the Echini, with a Revision of the Palaeozoic 
Species,” Mem. Boston Soc. Nat. Hist., vol. vii., 1912. 



244 



Proceedings of the Royal Society of Edinburgh. [Sess. 



horizontal diameter was 3’7 cm., its height 3*2 cm. It possesses five am- 
bulacral and five inter-ambulacral areas, but ambulacrum IV. (Loven’s nota- 
tion) has its apical extremity separated from the apical system by about 
1 cm., and possesses no corresponding ocular plate. The space intervening 
between the apex of the incomplete ambulacrum and the apical system is 
filled in by an aggregation of modified inter-ambulacral plates, more or 
less irregularly arranged, but with each individual plate approximately 
symmetrical about its longitudinal diameter. Retardation in the growth 



3 - 



-- CL 



lu- 




ll 



Fig. 1. — Incomplete Development in Amblypneustes ovum. Apical area and surrounding 

coronal plates x 4^. 

of this area seems to have had the effect of preventing the apical system 
from attaining its customary polar position, so that, though still centrally 
placed ( i.e . immediately above the mouth), it is overtopped in height by 
the upper parts of radial areas I. and II. The apical system, but for the 
absence of the ocular plate corresponding to the incomplete ambulacrum, 
presents the normal pentagonal sjunmetry. A minor irregularity appears 
in inter-ambulacral area V., where, about 1 cm. from the edge of the peri- 
stome, there is a small papillary excrescence about 4 mm. in diameter. 
This is due to modification in three of the inter-ambulacral plates, two of 
which are occluded, and the intercalation of three additional small demi- 
plates which give rise to the protuberance. 




1913-14.] Abnormal Echinoids in the Royal Scottish Museum. 245 

A general type of regulation occurs in the Echinus described by Ritchie 
and MTntosh (loc. cit.), where a simple increase in the length of the inter- 
ambulacral plates compensated for and bridged the potential gulf left by 
the disappearance of the ambulacrum. But here the mode of regulation 
is essentially different. It would seem that before the ambulacrum ceased 
to be formed some disturbance occurred in the growth area, for a couple of 
exceedingly large inter-ambulacral plates in proper series have been formed. 
Subsequently to the assumed damage the ocular plate was cast off or 
absorbed, and then a large growth area at the external margins of the two 
genital plates became continuous and gave rise to an enormous median, 
roughly triangular plate which succeeds the detached end of the ambul- 
acrum and terminates two half -rows of inter-ambulacral plates. The 
remaining space between this and the apical system is filled in, not by 
regular inter-ambulacral plates, but by a group of irregular casual plates, 
the group being roughly symmetrical about a median longitudinal axis. 

This type of regulation is a stage between the complete unharmed 
inter-ambulacral areas (exhibited in the Echinus esculentus described by 
Ritchie and MTntosh, or in areas 4 and 5 of the Amblypneustes recorded 
by Hawkins *), and the complete disappearance of a total ray, as occurs in 
the specimens recorded by Bell-)- and Philippi.!; 

Soft Parts. — So far as could be distinguished, the badly preserved 
genitalia presented the normal five-partite arrangement and contained 
male elements. 

(ii) Echinus esculentus, Linn. 

The specimen was obtained by Mr F. G. Pearcey in the Cromarty Firth 
at a depth between 8J to 16 J fathoms. It contained shrivelled female 
reproductive organs. Even in the dry condition in which it was preserved, 
when still covered with spines, it showed marked irregularity of outline. 
This in plan was trapezium-shaped. There was a distinct flattening of 
the test in the part which lay between the vertex and the long side of the 
trapezium, and the apical system was so distorted that it lay on this 
flattened surface, only one edge reaching up to the summit of the test. 
The maximum horizontal diameter of the test was 5 cm., its height 3 cm. 
There were the usual five teeth in Aristotle’s lantern. 

The spines having been removed, there was revealed the type of 
abnormality shown by the specimen of Amblypneustes described above, 
but in a more extreme degree; for here ambulacrum V. had almost dis- 

* Hawkins, Proc. Zool. Soc., 1909, part ii. p. 714, figs. 226-230. 

t Bell, Jour. Linn. Soc., vol. xv., 1881, p. 126, pi. v. 

\ Philippi, see Bateson, Materials for the Study of Variation , London, 1894, p. 443, fig. 137. 



246 Proceedings of the Royal Society of Edinburgh. [Sess. 

appeared (Plate, fig. 1). The peristome and mouth parts were normal, 
but in the apical system abnormality was strikingly apparent. The 
genital plates of areas 1, 2, and 3 (the last split into two segments) were 
present approximately in their normal positions, and associated with them, 
in the customary arrangement, were the oculars I., II., III., and IV. It is 
certainly remarkable that in spite of the spreading out of the plates 
surrounding the periproct not one of the oculars was “ insert.” The 
remainder of the periphery of the periproct was bounded by a single rank 

171 - 




Fig. 2. — Incomplete Development in Echinus esculentus. Apical area and surrounding 
coronal plates x 3 ; gen. 5, supposed 5th genital plate. 

of small plates, each more or less rectangular in outline, with several 
smaller triangular plates thrust in to complete the almost circular outline 
of the series. This abnormal series contained in all nineteen plates and 
demi-plates, with two additional small circular plates between ocular I. 
and the margin of the periproct. The plates were similar in size and 
shape, and the majority bore primary tubercles, but one, the third from 
ocular I., was perforated by a distinct pore and possibly represents genital 5, 
although in the dried state no genital products were associated with it. 
The madreporite was divided into two lobes, both perforate. 

Outside the ambulacral area the derangement and consequent regulation 
was exceedingly extensive. Apart from the one disturbed area, the 



1913-14.] Abnormal Echinoids in the Royal Scottish Museum. 247 

“ morphological units ” have remained intact, so that the left row of 
inter-ambulacrum 4 and the right row of inter-ambulacrum 5 were 
practically normal and were associated normally with the ambulacral areas 
in their respective “ arms.” On the other hand, the inter-ambulacral rows 
of arm V. bent away from their ambulacral area, the intervening space 
thus created being filled in by irregular small plates. But they ceased to 
exist at about the level of the truncated ambulacrum. Still a large area, 
measuring 12‘5 mm. in height from the termination of the truncated 
ambulacrum to the apical chain of plates, and 28 mm. from side to side, 
remained to be accounted for. This was filled in by a series of irregular and 
generally small plates arranged in lines roughly parallel to the circular 
periphery of the periproct. Considerable flattening has taken place in this 
growth area, which has thus been covered with the minimum of material. 

Of ambulacrum V. only about 1 cm. remained. The two pore rows, 
instead of approaching each other and meeting aborally to form a closed 
area, were parallel throughout, the open aboral end being filled in by small 
plates ; The individual rows of ambulacral plates in the disturbed area 
have suffered in different ways. The row to the left was perfect so far as it 
went as regards pore-pairs, but the right-hand row was shorter and for the 
latter half of its length was destitute of pores, except for three scattered and 
imperfect pore-pairs. 

Aristotle’s lantern was removed, and showed the normal skeletal 
arrangements. 

Soft Parts . — The dried remains of the soft parts were unsatisfactory. 
Three genital glands or portions of them were present, corresponding to the 
genital pores in areas 1, 2, and 3, but there was no trace of gland in 
connection with the abnormally situated pore supposed to be genital 5. 
The intestine was much broken, but it was noted that an upward loop in 
the middle of the abnormal area actually crossed the lower portion of the 
apical area, and that the intestine doubled on itself towards the anus in 
area 4, instead of, as usually occurs, in area 3. 

III. Total Variation from Five to Six-rayed Form. 

Echinus esculentus, Linn. 

Only one cake of this type has been observed in the collections — an 
example of Echinus esculentus, Linn., obtained in the Cromarty Firth by 
Mr F. G. Pearcey, at a depth between 8J and 16 \ fathoms. Examination 
of the shrivelled reproductive organs proves it to have been female. 

The specimen was preserved in a dry condition and, even clothed with 



248 Proceedings of the Royal Society of Edinburgh. [Sess. 

spines, it presented an unusually depressed appearance, the maximum 
diameter being 10 cm., the height 5 cm. Yet the hexradiate symmetry 
was so little apparent that it had escaped notice. 

On the test denuded of spines the presence of six ambulacra and 
six inter- ambulacra was very marked, depression in the inter-ambulacral 
areas giving the ambitus an approach to regular hexagonal shape. A 
peculiar feature is common to all the inter-ambulacral areas. These, 
instead of narrowing gradually towards their subtending genital plates, 
widen out about a centimetre from the summit, so that the recently formed 
plates are as large as, or even larger than, some of their predecessors. On 







Fig. 3. — Hexamery in Echinus esculentvs. Apical area x 2^ ; m, madreporite. 

the aboral surface hexamery is apparent in the peristome. Six teeth are 
present, the lantern itself is six-partite, the elements of the parts being 
normal, while the buccal tube feet are arranged in six pairs. 

The apical system, while presenting a hexradiate appearance, is less 
regular. The genital plates are five in number. Those in areas 2, 3, and 4 
(according to Loven’s system, and assuming that the madreporite retains its 
normal position in area 2) are normal in shape and position. Genital plate 
5 has a greater lateral diameter than usual ; opposite area 5 it is normal 
in shape, but it is continued for a short distance opposite area 6. The 
remainder of the apical system is filled in by a double plate which subtends 
both of the areas 1 and 6. This is practically equivalent to two normal 
plates laterally adnate. The genital pores are normal in position, there 



1913-14.] Abnormal Echinoids in the Royal Scottish Museum. 249 

being two individuals on the double plate. The pore on genital plate 3 
is doubled, the apertures being incompletely separated. 

There are six oculars. Those opposite ambulacral areas II., III., IV., 
and V. are normal in shape and position. Ocular VI. lies in a notch in 
genital 5, by which plate alone it is subtended ; and ocular I. lies in a 
similar notch opposite the middle of the double genital plate. Each of 
these is about half the usual size. 

The anus lies nearest to the right-hand corner of genital 5. 

The removal of Aristotle’s lantern disclosed the fact that, in the soft 
parts also, hexamery prevailed, for the reproductive organs were developed 
in six equal inter-radial rays. The alimentary canal, although longer than 
usual, followed the normal course even in detail, for the intestine doubled 
upon itself in inter-ambulacral area 2, and its last point of attachment was 
in inter-ambulacral area 3, as in normal specimens. 

Clear cases of spontaneous variation in the major symmetries of sea 
urchins are very rare. Of the most likely of such cases — those in which 
complete rays are added — few have been recorded, and still fewer have been 
satisfactorily described. As Bateson in his Materials for the Study of Varia- 
tion, 1894, mentions only two cases of “ total variation to a six-rayed form,” 
and as Jackson’s list (op. cih, 1912, p. 46) omits several recorded cases, we 
give the following short summary of all the examples of “total” hexamery we 
have been able to discover, with the view of simplifying future researches : — 

Recorded Cases of Total Hexamery. 

Regularia. 

(1) Amblypneustes sp. : hexamerous specimen (no further description). 
Haacke, Zool. Anz., 1885, p. 506. 

(2) Echinus eseulentus : 6 teeth, pairs of buccal tube feet, ambulacral 
and inter-ambulacral zones, ocular and genital pores, ocular and genital 
plates, two of the latter adherent — described in present paper. 

(3) Tripneustes eseulentus : 6 teeth, ambulacra and inter-ambulacra, 
oculars and genitals, two of the latter adherent. Jackson, Mem. Boston 
Soc. Nat. Hist., vol. vii., 1912, p. 46. 

(4) Toxopneustes lividus : 6 teeth, pairs buccal tube feet, ambulacra, 
genitals, and oculars. Ribaucourt, Gomptes rendus Ac. Sci., vol. cxlvi., 1908, 
p. 92. 

(5) Paracentrotus (Strong ylocentrotus) lividus (artificially reared) : 
6 teeth, terminal tentacles, and ambulacra. Delage, Gomptes rendus Ac. 
Sci., vol. cxlv., 1907, p. 546. 



250 



Proceedings of the Royal Society of Edinburgh. [Sess. 

(6) Strong ylocentrotus drobachiensis : 6 teeth, ambulacra, inter-ambu- 
lacra, oculars, and genitals, two of the latter adherent. Jackson, op. cit., 
p. 47. 

(7) Strongylocentrotus drobachiensis as No. 6. 

(8) Species unnamed — hexamerous specimen (no further description), 
seen by Ribaucourt and mentioned by him, loc. cit. 

Irregularia. 

(9) Galerites albogalerus : 6 ambulacra and inter-ambulacra. Meyer, 
Nov. Acta Ac. L. G. Nat. Cur., vol. xviii., 1836, p. 294, pi. xiii., figs. 6 
and 7. 

(10) Galerites sp., six-rayed. Laur., S. B. Ges. Isis, 1894, p. 6. 

(11) Pyrina ovulum : a sixth ray added at posterior, displacing periproct, 
6 oculars, 5 genitals. Seguin, Feuill. Nat., ser. 4, No. 376, 1902, p. 81, 
figs. 1 and 2. 

The descriptions of many of these specimens are insufficient to indicate 
whether or not the hexamerous arrangement prevailed in all the organs. 
As to the Pyrina ovulum recorded by Seguin, that author suggests that 
the addition of a fifth genital plate and corresponding ocular indicates a 
reversion to an earlier and more typical symmetry than that of Pyrina. 
Of those regular sea urchins which have been described with any attempt 
at detail, perfect hexamery appears to have prevailed in cases 4 and 5 of 
the above list, all the organs having been, so far as one can judge, perfectly 
formed. The origin of such cases cannot be further particularised than as 
due to spontaneous meristic variation. 

In the case of the Echinus esculentus here described the apical area 
gives a clue to the situation of the abnormality. Oculars II., III., IV., and 
Y. are similar in size, whereas the remaining two oculars resemble each 
other in being each about half the size of a normal individual. This fact, 
and the irregularity of the neighbouring genital plates, indicate that the 
additional areas were added in the right posterior segment. Further, the 
union between genitals 1 and 6 suggests that the latter is an imperfect 
double of the former, the imperfection of the duplication making necessary 
the abnormal compensatory extension of genital 5. We suggest, then, but 
with reserve, that this Echinus may represent a case of almost perfect redupli- 
cation of radii, inter-ambulacral area 1 and its flanking series of ambulacra 
being repeated in area 6 with its associated ambulacral series. If such be 
so, the present specimen comjDletes the series of already known cases of 
partial reduplication of radii (see Bateson, Materials for Study of Variation, 



1913-14.] Abnormal Echinoids in the Royal Scottish Museum. 251 

p. 446). Stewart has described an example of Amblypneustcs griseus, in 
which an ambulacrum only was imperfectly duplicated ; Cotteau a specimen 
of Hemiaster batnensis, in which an ambulacrum only was completely 
duplicated ; Gautier an Hemiaster latigrunda, in which an ambulacrum 
was completely duplicated and an inter-ambulacrum imperfectly ; and in 
the present Echinus esculentus both ambulacral and inter-ambulacral series 
show perfect duplication. 

Along with our Echinus must be reckoned the specimens of Tripneustes 
esculentus and Strongylocentrotus drobachiensis (two cases) described by 
Jackson; for in all of these, two of the six genital plates are adherent, 
apparently indicating again the residue of the almost perfect duplication 
of a ray. Regarding this curious phenomenon of two fused genitals with 
an ocular between them which he found in the only cases (three in number) 
of complete hexamery discovered amongst 50,000 sea urchins, Jackson 
says : “ It is certainly most extraordinary that this parallel structure 
should exist in three specimens, and indicates what I have elsewhere 
pointed out, how very definite extremely rare variation may be.” It adds 
to the wonder, and to the evidence of definiteness of particular variations, 
that the specimen above described, belonging to still a different genus from 
Jackson’s, should repeat for a fourth time in hexamerous Echini this 
curious abnormality. 

The evidence as to means of growth-compensation controverts the find- 
ings of Jackson, who found that £ ‘ in the six-rayed specimen [. Tripneustes 
but also in his other specimens] evidently the space gained to add the extra 
ambulacrum and inter-ambulacrum is attained by building ambulacra of 
practically the usual width, but narrowing all the inter-ambulacra equally 
to much less than the usual width. This emphasises the conclusion 
gathered from normal Echini that the inter-ambulacrum is essentially a 
space-filler and adapts itself to fill what space is available between the 
ambulacra which are the most essential structures.” In view of these 
statements the six-rayed Echinus was compared, as to relative proportions 
of ambulacra and inter-ambulacra, with a normal specimen of, as nearly as 
possible, the same size, with these results : — 





Circumference 
at Ambitus. 


Average Width 
of Inter-ambu- 
lacral Areas. 


Average Width 
of Ambulacral 
Areas. 


Normal Echinus 
Six-rayed Echinus . 


318 mm. 
314 mm. 


41 mm. 
33 mm. 


23 mm. 
19 mm. 



252 



Proceedings of the Royal Society of Edinburgh. [Sess. 

Clearly the ambulacral areas have suffered reduction here as well as the 
inter-ambulacral, and the extent of reduction in the two types of area is 
roughly proportional, the diameter relationship between the ambulacral 
and inter-ambulacral areas of the normal specimen being as 1 to 1*783, and 
of the six-rayed specimen as 1 to 1*737. The proportionally greater loss 
in diameter of the inter-ambulacra is obviously too small to support 
Jackson’s statement. 



EXPLANATION OF PLATE. 

Eoman and Arabic numbers mark the ambulacral and inter-ambulacral areas 
according to Loven’s notation. 

Eig. 1. Incomplete development in Echinus esculentus . Moray Firth specimen 
viewed from flattened, abnormal aspect, showdng the termination of imperfect 
ambulacrum V., the very numerous and irregular regulation plates or “space-fillers” 
in the corona, and the asymmetrical position and abnormal plates of the apical 
area. x 2. m = madreporite. 

Fig. 2. Hexamery in Echinus esculentus. Apical aspect of Moray Firth specimen. 
Natural size. 



(Issued separately September 4 , 1914 .) 



Proc. Roy. Soc. Edin. 



Vol. XXXIY. Plate I. 



Ritchie and Todd— Abnormal Echinoids. 




Photo, by James Ritchie. 



M'Farlane Erskine, Edin. 



1913-14.] 



Projection-Model of the 600-Cell. 



253 



XIX. — Description of a Projection-Model of the 600-Cell in Space 
of Four Dimensions. By D. M. Y. Sommerville, M.A., D.Sc., 
Lecturer in Mathematics, University of St Andrews. (With a Plate.) 

(Read May 4, 1914. MS. received June 1, 1914.) 

§ 1. In 1880 Stringham 1 proved that in space of four dimensions there 
exist six and no more regular rectilinear figures, whose boundaries are 
regular polyhedra. The same result was arrived at independently by 
Hoppe 2 in the following year. In 1883 Schlegel 3 gave an extensive 
investigation of the same problem, and constructed projection-models of 
the six regular figures, which were exhibited at the Magdeburg meeting 
of the Society of German Naturalists in 1884. This series of models was 
published by the firm L. Brill of Darmstadt and is obtainable from their 
successors, Martin Schilling in Leipzig. 

The models are constructed of brass wire and silk threads, and represent 
projections of the figures in ordinary space in such a way that there is no 
overlapping of boundaries. In each case the external boundary of the 
projection represents one of the solid boundaries of the figure. Thus the 
600-cell, which is the figure bounded by 600 congruent regular tetrahedra, 
is represented by a tetrahedron divided into 599 other tetrahedra ; 20 
tetrahedra meet at every vertex and 5 at every edge; 12 edges meet at 
each point; the total number of vertices is 120. At the centre of the 
model there is a tetrahedron, and surrounding this are successive zones of 
tetrahedra. The boundaries of these zones are more or less complicated 
polyhedral forms, cardboard models of which, constructed after Schlegel’s 
drawings, are also to be obtained from the same firm. 

§ 2. The model which was constructed and exhibited by the present 
writer represents an exact stereographic projection of the 600-cell, i.e. the 
centre of projection is taken on the circumscribed hypersphere, and in fact 
is one of the vertices of the figure. The projection of this vertex would 
therefore be at infinity, and the 12 edges which meet there would be 
represented by lines proceeding to infinity from the vertices of the regular 
icosahedron, which is the outermost accessible boundary of the projection, 

1 “ Regular Figures in ^-dimensional Space,” Amer. J. Math., 3, 1-14. 

2 “ Regelmassige linear begrenzte Figui en von vier Dimensionen,” Arch. Math., Leipzig, 
67, 29-44. 

3 “ Theorie der homogenen zusammengesetzten Raumgebilde,” Halle, Nova Acta Acad. 
Leo'p., 44, 343-459. 



254 



Proceedings of the Royal Society of Edinburgh. [Sess. 



In the model these infinite edges have been omitted, so that the model is 
to that extent incomplete. The projection of the vertex which is opposite 
the centre of projection forms the centre of the model, and the successive 
zones of vertices are very simple and regular. Starting from the outside — 

Zone A is the vertex at infinity (1 vertex). 

Zone B is a regular icosahedron (12 vertices). 

Zone C is a regular dodecahedron (20 vertices). 

Zone D is a regular icosahedron, whose vertices are not joined to one 
another. In the model these vertices are joined to the vertices of zone C 
by wires painted black, forming pyramids on the faces of the dodecahedron 
(12 vertices). 

Zone E, the mesial zone, is the semi-regular polyhedron called the 
icosidodecahedron, which is bounded by 20 triangles and 12 pentagons 
(30 vertices). 

Zone — D is similar to zone D, and its vertices are joined by black wires 
to the vertices of zone — C, forming pyramids on the faces of a dodecahedron 
(12 vertices). 

Zone — C is similar to C, i.e. a regular dodecahedron (20 vertices). 

Zone — B is similar to B, i.e. a regular icosahedron (12 vertices). 

Zone — A is the centre (1 vertex). (Total number of vertices 120.) 

The edges which join up the vertices of each zone are of brass wire, 
and, with the exception of the edges joining zones C, D, and — C, — D, the 
edges joining different zones are of differently coloured silk threads. All the 
threads which join the vertices of the same two zones, and those of the cor- 
responding zones on the other side of the mesial zone, are of one colour. 

§ 3. The model has been constructed so that the radius of the circum- 
scribed hypersphere is 8 cm. 

In making the calculations for the lengths of the edges great use has 
been made of Schoute’s valuable paper, 1 which gives the co-ordinates of the 
120 vertices in the most symmetrical form, and tabulates the connecting 
edges. In Schoute’s system of numbering, the 120 vertices are numbered 
from 1 up to 60, and from — 1 to — 60 for the opposite vertices. With 
reference to the special arrangement of the vertices in the stereographic 
projection, whereby one vertex is singled out as centre of projection, 
another system of numbering allows of a more compact table of connecting 
edges. The vertices of each zone are numbered separately, and so also are 
the rings or zones of vertices of each zone. A pair of opposite vertices of 

1 “ Regelmassige Schnitte und Projectionen des Hundertzwanzigzelles und Sechs- 
liundertzelles im vierdimensionalen Raume,” Amsterdam, Verh. K. Akad. Wet. (le. Sect.), 
II. No. 7 (1894). 



255 



1913-14.] Projection-Model of the 600-Cell. 

any zone are numbered ±n. Thus, e.g., B 3 and — B — 3 denote opposite 
vertices of the 600-cell. For the mesial zone — E is the same as E, and 
— E 3 is the same as E 3. 

In zones B and D, the icosahedra, the vertices are numbered 0 ; 1, 2, 3, 
4, 5; -1, -2, -3, -4, -5; 0. 

In zone C, the dodecahedron, they are numbered 1, 2, 3, 4, 5 ; 1 , 2 , 3 , 
4 , 5 ; - 1 , - 2 , - 3 , - 4 , - 5 ; -1, -2, -3, -4, -5. 

In zone E, the icosidodecahedron, they are numbered 1, 2, 3, 4, 5; 
1 , 2 , 3 , 4 , 5 ; 13, 24, 35, 41, 52, -13, -24, -35, -41, -52 (or 31, 42, 53, 
14, 25); etc.; i.e. the 10 vertices of the equator of this zone are represented 
by the pairs of numbers which represent the vertices of the adjacent rings 
to which they are connected, and 31 is the same as —13. 

§ 4. In order that reference may be made to Schoute’s tables, Table I. gives 
the numbers in the present system, which correspond to Schoute’s numbers. 
No. 4 of his system, which is on the axis of w, is taken as centre of projec- 
tion. Then — 4 is — A, the centre of the model. The numbers corresponding 
to the negative numbers of Schoute’s system are obtained by changing B, 
C, D into — B, — C, — D, and changing the sign of the number. 

Table II. gives the edges of the 600-cell. 

Table III. gives the co-ordinates of the vertices, according to Schoute, 
but the plane of x, y, z has been moved so as to pass through A, i.e . w has 
been changed into 2 (e + lj-m The symbol e = j5. 

Table IV. gives the lengths of the edges of the projection. 

§ 5. In the projection a number of groups of points become coplanar. 
These are the projections of points which lie in the same hyperplane 
passing through the centre of projection. The groups of points in the 
original figure which are so projected form zones of the same form as the 
zones B, C, D, E, and their centres lie in the zones B, G, D, E respectively. 
Thus, taking the point BO as centre, we have the icosahedron — 

A; B 1, 2, 3, 4, 5; C 1, 2, 3, 4, 5; BO, j 

which is projected into a plane figure. 

With centre Cl we have first the icosahedron — 

B 0, 3, 4 ; C 1, 2, 5 ; B 0, 3, 4 ; E 1, 3, 4, 
and next the dodecahedron — 

A; B - 1, 2, 5; C 3, 4, 2, - 3, - 4, 5 ; 

-Cl; - B 0, 3, 4 ; E, 2, 5, 2, 5, 13, 14, 



and this last is projected into a plane figure. 



256 



Proceedings of the Royal Society of Edinburgh. [Sess. 

With centre DO we have the icosahedron — 

BO; Cl, 2, 3, 4, 5; E 1, 2, 3, 4, 5 ; -DO; 
the dodecahedron — 

B 1, 2, 3, 4, 5 ; D 1, 2, 3, 4, 5 ; E 1, 2, 3, 4, 5 ; -Cl, 2, 3, 4, 5 ; 
and the icosahedron — 

A ; C 1, 2, 3, 4, 5 ; - D 1, 2, 3, 4, 5 ; -BO, 

and the last figure becomes a plane figure in the projection. 

With centre El we have the icosahedron — 

C3,4; D 0, 1 ; E 2, 5, 3, 4 ; - D 0, 1 ; - C 3, 4, 
the dodecahedron — 

BO, 1; C 2, 5, 3, 4 ; D 2, 5 ; E 3, 4, 31, 41 ; 

-BO, 1; -02,5,3,4; -D 2, 5; 
the icosahedron — 

B 2, 5 ; C 1, - 1 ; E 2, 5, 35, 42 ; - C 1, - 1 ; - B 2, 5 ; 
and the icosidodecahedron — 

A; B3,4, -3, -4; C 2, 5, - 2, - 5 ; D 3, 4, - 3, - 4 ; El, - 1,25,52; 

- A ; - B 3, 4, - 3, - 4 ; - C 2, 5, - 2, - 5 ; - D 3, 4, - 3, - 4, 

the latter being projected into a plane figure. 

§ 6. The equations of transformation for the stereographic projection 
with centre at the point A, i.e. the origin, and plane of projection w = 
2 (e + 1), are : 

x _ y _ z _ 2(e + 1) 
x' y z w' 

where x', y', z', w' are the co-ordinates of a vertex of the 600-cell and x, y, z 
those of its projection. 



Table I. — Notation for the 120 Vertices of the 600-cell, (a) Schoute’s 
Notation, ( b ) Notation used in the Present Paper. 



a. 


b. 


a. 


b. 


a. 


b. 


a. 


b. 


a. 


b. 


1 


E 


52 


13 


B 


0 


25 


B 


2 


37 


B 


3 


49 


E 


2 


2 


E 


1 


14 


B 


1 


26 


B 


5 


38 


B 


4 


50 


E 


5 


3 


E 


1 


15 


B- 


1 


27 


B- 


5 


39 


B- 


4 


51 


E 


4 


4 


A 




16 


-B 


0 


28 


-B 


2 


40 


-B 


3 


52 


E 


-3 


5 


C 


5 


17 


C 


1 


29 


D 


2 


41 


C 


5 


53 


E 


5 


6 


c 


2 


18 


C- 


1 


30 


D 


5 


42 


C 


2 


54 


E 


2 


7 


c 


4 


19 


C 


1 


31 


D- 


5 


43 


C- 


2 


55 


E 


42 


8 


c- 


-3 


20 


-c 


1 


32 


-D 


2 


44 


-c 


5 


56 


E 


53 


9 


-c 


5 


21 


D 


0 


33 


C 


4 


45 


D 


3 


57 


E 


3 


10 


c 


3 


22 


D 


1 


34 


c 


3 


46 


D 


4 


58 


E 


4 


11 


0- 


-4 


23 


D- 


1 


35 


c- 


3 


47 


D- 


■4 


59 


E 


41 


12 


-C 


2 


24 


-D 


0 


36 


-c 


4 


48 


-D 


3 


60 


E 


13 



1913-14.] 



Projection-Model of the 600-Cell. 



257 



Table II. — The Edges of the 600-cell. 



(To complete the table (1) perform a cyclic permutation of the numbers 1, 2, 3, 4, 5 in each 
row, keeping 0 unaltered ; (2) change the sign of every number in a row ; (3) change A, B, 0, D 
into - A, — B, - C, - D and vice versa.) 



A joined to each B. 

B 0 joined to A ; B 1, 2, 3, 4, 5 ; C 1, 2, 3, 4, 5 ; D 0. 

1 „ „ A; BO, 2, -3, -4, 5; C-l, 3,4, 3,4; D 1. 

Cl „ „ B 0, 3, 4 ; C 1, 2, 5 ; D 0, 3, 4 ; E 1, 3, 4. 

1 „ „ B- 1,3, 4; Cl, -3,-4; D - 1, 3, 4; El, 13, 14. 

DO „ „ B 0 ; C 1, 2, 3, 4, 5 ; E 1, 2, 3, 4, 5 ; - D 0. 

1 „ „ Bl; C-l, 3,4,3, 4; E 1, 31, 41, 3, 4 ; -Dl. 

El „ „ C 3, 4 ; D 0, 1 ; E 2, 5, 3, 4 ; - D 0, 1 ; - C 3, 4. 

1 „ „ Cl, 1; D 3,4; E3, 4,13,14; -D 3,4; -Cl, 1. 

13 „ „ C 1,-3; D- 1,3; El,- 3, 53, 14; -D-l, 3; -Cl, -3. 



Table III. — Co-ordinates of the Vertices of the 600-cell. Edge = 4. 

(The order of the combinations of sign, corresponding to the vertices going from left to 

right in a row, is + + , 4 — , — f, . To complete the table change all the signs in 

each row.) 



‘ 


X 


y 


z 




X 


y 


z 


A : w=0 
- A : w = 4(e + 1) 


1 ° 


0 


0 


D : w= 2e ; - I) : w= 2e + 4 


B : w=e- 1 ; -B:w=3e + 5 


0, 1 

2, -5 

3, 4 


0 

e + 3 

— (e + 1) 


— (e + 1) 
0 

e + 3 


e + 3 
±(e + l) 
0 


oohoc) 

i 

H 


0 

e + 1 
±2 


+ 2 
0 

e + 1 


e+1 

±2 

0 


E : w = 2(e + 1) 


C : w=e + 1 ; -C : -M? = 3(e+1) 


52 

1 

1 

3, 13,41,- 4 

2,- 3, 5,- 4 
5, 42, 2, 35 


2(e+ 1) 
0 
0 
2 

±(e+l) 
±(e + 3) 


0 

2(e+l) 

0 

±(e + 3) 
2 

±(e + l) 


0 

0 

2(e+ 1) 
±( e + 1) 
± ( e + 3) 
2 


1, 1 

4, 3 

5, -2 
5, 2 

-3,-4 


0 

±2 
e + 3 
±(e+l) 
±(e + l) 


e + 3 
0 

±2 
e+1 
e + 1 


±2 
e + 3 
0 

e + 1 

-(e+1) 



VOL. XXXIV. 



[Table IV. 

17 



258 



Proceedings of the Eoyal Society of Edinburgh. [Sess. 



Table IV. — Lengths of Edges of the Projection of the 600-cell. 



Joining 

Zones. 


No. of 
Edges. 


Length of Edge, when— 




Edge of 
600-cell = 30. 


Radius of Circumscri 
= 30. 


ibed Hypersphere 
= 1. 


- B to - 


B 


30 


6(5 - e) 


6(3e— 5) 


0-3416 


-o „ - 


C 


30 


20 


10(e-l) 


0-4120 


-C „ - 


•D 


60 


10(e-l)V3 


10(3 - e)V3 


0-4411 


E „ 


E 


60 


30 


15(e - 1) 


0-6180 


B „ 


C 


60 


6e\/10 + 2e 


6e\/10 - 2e 


1*0515 


G „ 


C 


30 


60 


30(e - 1) 


1-2361 


B „ 


B 


30 


30(3 -fe) 


30(e + 1) 


3-2361 


B „ 


A 


12 


oo 


00 


00 


-A „ - 


B 


12 


3\/10(5 - e) 


6eV5 - 2e 


0-3249 


-B „ - 


C 


60 


2e\/6(5 - e) 


4 VI 5(5 -2e) 


0-3752 


-B „ - 


D 


12 


12e\/5 - 2e 


6e 50 — 22e 


0-4016 


-c „ 


E 


60 


10V6 


5(e — l)V6~ 


0-5046 


-D „ 


E 


60 


15(e-l)V2 


15(3 - e)V2 


0-5402 


-B „ 


D 


12 


6eVlO-2e 


12eV5-2e 


0-6498 


E „ 


D 


60 


6e\/5 + e 


6eV& - e 


0-7435 


E „ 


C 


60 


30V2 


15(e - 1)V2 


0-8740 


D „ 


B 


12 


12e\/5 + 2e 


6eV10 + 2e 


1-7013 


0 „ 


B 


60 


30(1 + e) 


60 


2-0000 



The accompanying plate represents a symmetrical orthogonal plane 
projection of the three-dimensional projection on exactly \ the scale of the 
model. Zones B and — B are in black, C and — C are in red, and E is in 
blue. The vertices are denoted as in the text, but for compactness the 
“ minus ” is put as a mark over the letter or number. 



{Issued separately September 29, 1914.) 



SOMMERVILLE: FOUR DIMENSIONAL FIGURE. 




1913-14.] Resistance of Iron in Crossed Magnetic Fields. 259 



XX. — Changes of Electrical Resistance accompanying Longi- 
tudinal and Transverse Magnetizations in Iron and Steel. By 
Professor C. Gr. Knott, D.Sc. 

(Read May 4, 1914. MS. received October 1, 1914.) 

In t January 1913 I communicated a paper on the changes of resistance of 
nickel when subjected to a combination of longitudinal and transverse 
magnetic fields (1). The following paper contains an account of exactly 
similar experiments with iron and steel. 

Each steel or iron strip formed the core of an anchor-ring coil which 
was double-wound, with two exactly equal coils of copper wires. When 
the current was passed through the two contiguous coils in series in the same 
direction the metal cores were magnetized longitudinally. When the current 
was passed in opposite directions through the two coils there was no 
magnetization produced in the cores, but the heating effect was the same 
as in the first case. At the beginning of each experiment the current was 
applied in the latter or unmagnetizing arrangement, and was sustained for a 
sufficient time to permit the temperature to become practically constant. 
With reversal of the current in the one half of the enveloping coil a longi- 
tudinally magnetizing force was established within the region occupied 
by the iron or steel core. By means of a succession of reversals and re- 
reversals the core could be subjected to a cyclical variation of magnetizing 
force, while the temperature remained practically constant. 

Six layers of the magnetizing coil were wound round each core, the 
number of windings in each layer being in accordance with the following 
table. 



Layer. 


Number of Windings 


in Magnetizing Coil. 


Steel Core. 


Iron Core. 


I. 


156 


184 


II. 


130 


176 


III. 


120 


184 


IV. 


128 


180 


V. 


112 


186 


VI. 


160 


180 


Total Windings 


806 

. 


1090 



260 



Proceedings of the Royal Society of Edinburgh. [Sess. 

The steel core formed a circle of 6 cm. diameter, and the iron core one of 
7*3 cm. diameter. The larger size of the iron core accounts for the greater 
number of windings in each layer. 

Applying the usual approximate formula, we find that a current of one 
ampere passing through the magnetizing coils will produce fields of 53*7 
and 59*6 in the steel-core and the iron-core anchor-ring respectively. 

The transverse field was applied by means of a specially designed 
electromagnet with cylindrical pole pieces, the air gap between which 
could be altered with ease. The anchor-ring coil under investigation was 
placed symmetrically in the air gap, so that the axis of the anchor-ring 
passed through the centres of the pole pieces. The magnetic fields 
established in the air gap for various lengths of air gap and strengths of 
current passed through the coils of the electromagnetic were measured by 
means of a Grassot Fluxmeter. The lines of force established in the air 
gap ran across the coiled strip of iron or steel, that is, transverse to the 
direction in which the resistance was being measured. 

The method of experimenting was identical with that described in 
detail in the former paper (1). 

The iron or steel strip formed the greater part of one arm of a Wheat- 
stone Bridge, an approximate balancing being secured by adjustment of 
the point of contact on a stretched wire. The combined system of con- 
ductors forming the Wheatstone Bridge was made part of a circuit 
through which a small steady current was passed from a secondary cell. 
When this current was flowing steadily through the circuit, one of the 
known resistances in the Bridge was altered slightly in a definite manner 
by introducing a large resistance shunt in parallel with this resistance. 
The deflection obtained on the galvanometer, being due to a measurable 
disturbance in the balance, was essentially a standardizing of the deflec- 
tion. This calibrating shunt being thrown out of connection, the iron or 
steel strip which formed the opposing branch in the Bridge was then 
magnetized. The disturbance due to this cause at once declared itself by 
a corresponding deflection on the galvanometer scale. This deflection, 
taken in conjunction with the deflection formerly produced in the standard- 
izing experiment, gave the means of calculating the change of resistance 
accompanying a given magnetization. 

The galvanometer used in these experiments was a D’Arsonval galvano- 
meter of the Ayrton-Mather design, and was found eminently satisfactory 
on account of its steadiness and sensitiveness. 

As in the previous experiments with nickel, the deflections were obtained 
by reversing the steady current through the Wheatstone Bridge, the 



1913-14.] Resistance of Iron in Crossed Magnetic Fields. 261 

reading produced when the current was in the one direction being sub- 
tracted from the mean of the readings immediately preceding and succeed- 
ing with the current in the other direction. Five successive sets of such 
triplets of readings were taken as quickly as possible : (1) with no magnetiz- 
ing force applied, (2) with the magnetizing force applied in, say, the positive 
direction, (3) with no magnetizing force applied, (4) with the magnetizing 
force applied in the negative direction, (5) with no magnetizing force 
applied. Each triplet gave a first difference of deflections ; and from the 
five first differences two second differences were obtained by subtracting the 
second from the average of the first and third, and the fourth from the 
average of the third and fifth. The average of these two second differences 
was the final value of the deflection due to the application of the magnetis- 
ing force. By means of the standardizing experiment this final value was 
reduced to absolute measure in the form c^N/N, where N is the resistance 
of the iron or steel strip. 

The calibration experiment involved the observation of at least nine 
distinct readings ; and the final value of the deflection in the experiment 
just described involved fifteen distinct readings. Hence the value of any 
one of the ratios, c?N/N, is deduced from twenty-four distinct galvanometer 
readings. 

A complete set of observations for any given pair of fields, the one 
longitudinal and the other transverse, required four groups of the fifteen 
readings just described. The first group was obtained with no transverse 
field, the longitudinal field being put on and removed twice with change of 
direction between the first and second applications. In the second group 
the transverse field was applied and kept steadily in action, the longitudinal 
field being put on and off with reversal of direction as before. In the third 
group the longitudinal field was kept steadily applied in its turn, and the 
transverse field was put on and off exactly as the longitudinal field was 
manipulated during the first and second groups. Finally, in the fourth 
group the longitudinal field was thrown off altogether and the transverse 
field applied and removed by itself in a cyclic manner, as was done with 
the longitudinal field in the first group. 

The field which was put on and off with reversal of direction is dis- 
tinguished as the “ cyclic field ” ; and the other, which for the time is being 
maintained, is called the “ steady field.” 

For other details of the method, and for the investigation of the complete 
theory, reference may be made to the earlier paper. 

In the Appendix, which contains all the measured values of the changes 
of resistance, and in what follows here, the horizontal field will be re- 



262 Proceedings of the Royal Society of Edinburgh. [Sess. 

presented by h and the transverse field by t. The corresponding changes of 
resistance will be represented by capital letters H and T in accordance with 
the following convention. 

The four changes of resistance which form one set will be H, H(T), T, 
T(H), with the meanings 

H = effect of cyclic h, no transverse field existing; 

H(T) = „ „ „ h superposed on steady transverse field ; 

T= „ „ „ t, no longitudinal field existing ; 

T(H) = „ „ „ t superposed on steady longitudinal field. 



Results for Steel: dN/NxlO 4 . 



Longitudinal 

Field. 




i 

Transverse Fields in ( ). 






(864) 


(1282) 


(2141) 


(3781) 


(53-7) 


H 


4- 2*84 


+ 2-72 


4- 2-77 


4- 2-89 


H(T) 


4- 0*3 


+ o-i 


4- 0-19 


4- 0-01 




T 


- 4*59 


- 5-53 


- 6-29 


- 7-05 




T(H) 


- 7"55 


- 9-12 


- 9-86 


- 1037 






(843) 


(1268) 


(2111) 


(3706) 


(104) 


H 


4- 5T5 


+ 5-19 


4- 5-29 


+ 4-75 


H(T) 


+ 0-86 


+ 0-31 


4- 0-29 


+ 0-22 




T 


- 4-44 


- 5-64 


- 6'31 


- 6-73 




T(H) 


-10-34 


-11-39 


-12-25 


-12-4 






(606) 


(1268) 




(3706) 


(157) 


H 


*+ 6-47 


+ 6-69 




. + 6-45 


H(T) 


+ 3-12 


4- 1-08 




4- 0*5 




T 


- 3-99 


- 5-91 




- 6-77 




T(H) 


- 7-75 


- 12-53 


... 


-14-3 



Results for Iron: dN/N x 10 4 . 



Longitudinal 

Field. 




Transverse Fields in ( ). 






(898) 


(1282) 


(2156) 


(3796) 


(59-6) 


H 


4- 3-83 


+ 4-58 


4- 3-76 


4- 3-79 


H(T) 


4- 1-17 


4- 0-49 


4- 0-36 


4- 0-04 




T 


- 2-7 


- 5-48 


- 7-84 


- 8-98 




T(H) 


- 4 92 


-10-11 


-11-51 


-12*46 








(1282) 


(2156) 


(3781) 


(120-4) 


H 




+ 6-25 


+ 6-83 


+ 6-24 


H(T) 




4- 2-43 


+ 0-52 


+ 0-09 




T 




- 5-73 


- 7-97 


- 9-41 




T(H) 




- 10-83 


- 13-0 


-15-8 



1913-14.] Resistance of Iron in Crossed Magnetic Fields. 263 

The various values are tabulated in the foregoing tables. The bracketed 

o o 

numbers in the first column on the left give the values of the longitudinal 
fields ; and the bracketed numbers in the horizontal rows give the values 
of the transverse fields. The remaining numbers are the changes of resist- 
ance produced by the field or combination of fields indicated by the symbol 
in the second column. 

In these experiments there is no evidence of what others have observed, 
namely, an increase of resistance in low and moderate transverse fields. 
For example, Grunmach (2), in three out of the four recorded experiments 
with iron, obtained increase of resistance up to fields of 7000 or 8000 Gauss, 
after which the change became a decrease rapidly increasing in value as 
the field was taken stronger. In like manner, he obtained with nickel an 
increase of resistance up to field 700, and thereafter decrease as the trans- 
verse field was made stronger. 

I have always been very doubtful of the reality of this initial increase 
of resistance ; and a recent paper by Messrs W. Morris Jones and 
J. E. Malam (3) seems to me to establish the fact that when nickel is ac- 
curately placed in the transverse field the change of resistance is always a 
decrease. In my own earlier experiments with nickel spirals in transverse 
fields I was never satisfied that I had the spiral absolutely perpendicular 
to the field until I had got rid of this apparent initial increase in low fields. 
When very thin wires are used, the difficulty of eliminating all chance of 
a resolved longitudinal effect becomes greatly increased. For the change 
of resistance depends undoubtedly upon the magnetization within the 
metal. In very thin wires the transverse magnetization cannot be very 
much greater than the transverse magnetizing force, whereas in the 
early stages the longitudinal magnetization is much greater than the 
longitudinal magnetizing force. A little consideration will show that 
a comparatively small resolved component of the magnetizing force along 
some part of the wire may easily be accompanied by a longitudinal 
magnetization large enough to produce a resistance change of positive 
sign able to overbalance the very small decrease due to the transverse 
magnetization. 

All this danger of having present an uneliminated longitudinal com- 
ponent is obviated in the experiments now described by the use of ribbons 
instead of wires of iron and nickel. For in the first place it is a compara- 
tively simple matter to set the coiled strip or ribbon with its width 
accurately along the lines of force ; and in the second place, even if the ad- 
justment were not quite accurate, the magnetization along the width of the 
metal would be considerable, so that any possible resolved longitudinal 



264 



Proceedings of the Royal Society of Edinburgh. [Sess. 

effect would not be large enough to mask the effect of the transverse 
field. It seems to me, therefore, that attempts to explain the supposed 
increase of resistance in low transverse fields are quite uncalled for. 
What requires theoretical explanation is the decrease of resistance of 
both iron and nickel in transverse fields, and the increase of resistance 
in longitudinal fields. 

This conclusion receives further support that in the case of cobalt 
Grunmach (2) obtained only a decrease of resistance. The cobalt was not 
in the form of a thin wire, hut was a strip 02 mm. thick and 0*5 mm. broad 
coiled in a double flat spiral. With such a form there was less chance of 
error of adjustment. Consequently no increase of resistance was obtained 
in the lower fields. 

With the doubtful exception of tin in the lowest field, all the other 
metals experimented with by Grunmach showed increase of resistance in 
transverse fields (2). These metals were silver, cadmium, tantalum, 
platinum, tin, gold, palladium, zinc, copper, and lead. 

Through the kindness and by the help of Principal A. Crichton Mitchell, 
late of Travancore, I am able to add to these mercury. Professor Mitchell 
prepared a thin mercury column in a spiral glass tube of a convenient size 
to be inserted in the air-gap of the electromagnet which I used for 
establishing the transverse fields in the present experiments. Substituting 
the mercury spiral for the iron or steel ribbon in the arrangement described 
above, I measured the change of resistance in four different fields. The 
results are given in the following short table, in which the first row gives 
the values of the transverse -field in Gauss, and the second the correspond- 
ing changes of resistance per 10,000. 



Change of Resistance of Mercury in Transverse Magnetic Fields. 



Tranverse Field. 


2064 


3801 


5263 


6473 


cZR/R. 10 4 


+ 0T1 


+ 0-31 


+ 0-43 


+ 0-64 



The relation between these sets of numbers is not linear, nor does a 
parabolic law satisfy them very satisfactorily. Nevertheless, assuming the 
formula dR/R = Af 2 , where t is the transverse field, we find 

A = 1'7 x 10~ 12 , 

a result of the same order as for other non-magnetic metals. 

[Note added November 19, 19 — My attention has been drawn to a 
paper published in 1910 in the Nuovo Cimento (5), in which Dr G. Rossi 



1913-14.] Resistance of Iron in Crossed Magnetic Fields. 265 

gives certain results for the change of resistance of mercury in a transverse 
magnetic field. Treating his numbers in the same way, I find that A 
has the value 6 x 10~ 13 or 5 x 10 -13 for mercury filaments of diameter 
0-7 mm. or 0'5 mm. respectively. The diameter of the mercury filament 
used in the experiment just described was almost exactly 1 mm. The 
discrepancies are considerable ; and j Jo is difficult to believe that the effect 
in mercury should depend on the diameter of the filament within the 
limits indicated.] 

Now in field 3750 the corresponding changes of resistance per 10,000 in 
iron and steel are respectively — 6 ‘9 and —9*2, that is, twenty or thirty 
times the numerical value for mercury. 

In the earlier experiments with nickel the highest transverse field 
reached was only 815 ; but it was obvious that in much higher fields the 
change of resistance would not exceed the value — 95 x 10 -4 , that is, about 
ten times the value for steel. Changes numerically equal to those given 
above for iron and steel were obtained for nickel in fields of only twenty 
and thirty Gauss respectively. 

It is well to bear in mind that, as proved in the earlier paper, the 
numerical value of the change due to a given transverse field is a function 
of the width of the strip of the magnetic metal, for the simple reason that 
on that width also depends the value of the magnetization. 

I now pass on to the consideration of the main object of the research, 
namely the influence of a steadily maintained magnetic field upon the 
changes of resistance due to a cyclically applied field at right angles to the 
former. 

With regard to the numbers given in the Table three pages back, it 
should be noted that the last figure in the measured changes of resistance 
is of no value, being well within the limits of experimental error. 

The smaller number of data for the iron strip was due to the overheat- 
ing of the magnetizing coil round the strip and the consequent breaking 
down of the insulation between the contiguous turns of the coil. But the 
nature of the results is obviously the same in both metals, and may be 
expressed qualitatively in the following words : — 

1. Under the influence of longitudinal magnetization the electric resist- 
ance of iron and steel is increased ; but this increase is notably diminished 
when the longitudinal magnetizing force is superposed cyclically upon a 
steadily sustained transverse magnetization. In the highest transverse 
fields used the change of resistance due to the superposed longitudinal field 
was in most cases very small, being a small fraction of the value when the 
longitudinal field acted alone. 



2 66 Proceedings of the Royal Society of Edinburgh. [Sess. 

2. Under the influence of a transverse magnetization the electric resist- 
ance of iron and steel is diminished ; and this diminution becomes markedly 
greater when the transverse field is superposed cyclically upon a steadily 
maintained longitudinal field. In certain cases the change of resistance 
due to the transverse magnetizing force was more than doubled when this 
field was superposed upon the steadily maintained longitudinal field. 

It will be seen on referring to my earlier paper on the behaviour of 
nickel under crossed magnetic fields (1) that as regards the effect of the 
steady longitudinal field upon the change of resistance accompanying the 
application of a transverse field, exactly the same kind of phenomena are 
obtained with the iron and steel. 

On the other hand, as regards the effect of the steady transverse field upon 
the change due to the superposed longitudinal field, there was a peculiarity 
in the behaviour of nickel which is not found in the case of iron or steel. 
This peculiarity was that when the steady transverse field was above a 
certain value the change of resistance due to the superposed longitudinal 
field altered in sign, that is, the resistance was diminished, not increased. 

In the earlier experiments with nickel the arrangements did not permit 
the application of such large fields as were possible in the later experiments 
with iron and steel. Yet much greater values of the resistance change 
were obtained with the nickel than with the iron or steel, although these 
were subjected to much higher magnetizing forces. This will appear from 
the comparisons made in the short table below, in which -the changes of 
resistance in practically the same strengths of magnetizing fields are set 
side by side. The approximate values of the fields are given below each 
group of measurements. 



Changes of Resistance per 10,000. 





Longitudinal Field Cyclic. 




Transverse Field Cyclic. 


Nickel. 


Steel. 


Iron. 


Nickel. 


Steel. 


Iron. 


H 


+ 66 


+ 2-8 


+ 3-7 


T 


- 91 


-4*3 


-2-7 


H(T) 


-17 


+ 0-3 


+ 1*2 


T(H) 


-192 


-7-6 


-4-9 


h= 


60 


54 


60 


t = 


800 


700 


900 


t = 


800 


800 


900 


h 4 


60 


54 


60 



The main features of the phenomena here described are contained in 
this short table. The similarity of the effects produced in iron and nickel 
suggests that we are dealing with a fundamental property of ferromagnetic 



1913-14.] Resistance of Iron in Crossed Magnetic Fields. 267 

substances ; but of this we cannot be certain until the same experiments 
have been carried out with cobalt. I hope also to be able to make a similar 
study of the properties of bismuth. Meanwhile, I leave over any further 
theoretical discussion. I cannot, in fact, add anything to what was said in 
the earlier paper ; and I am not aware that anyone has been able to make 
even a plausible suggestion as to the molecular mechanism on which these 
phenomena in crossed magnetic fields depend. 

My thanks are due to Miss J. G. Dunlop and Miss M. Jazewska, who 
determined for me with great care the change with temperature of the 
resistance of the iron ribbon. 



Appendix. 

Results as reduced in Laboratory Note-Book, arranged approximately 
ACCORDING TO DATE IN THE YEAR 1913. 

The numbers in the columns headed Resistance Change give the changes of resistance, 
estimated per 10,000, of the metal strip. 

h and £ represent respectively the longitudinal and transverse fields. 

The temperatures are calculated from the resistances of the metal ribbon. 

Iron. 



Date, 

Fields, 

Temp. 


Cvclic 

Field. 


Steady 

Field. 


Resistance 

Change. 


Date, 

Fields, 

Temp. 


Cyclic 

Field. 


Steady 

Field. 


Resistance 

Change. 


July 22 


h 


None 


+ 


3-69 










h= 59-6 


h 


+ £ 


+ 


1T2 










£ = 898 


h 


-£ 


+ 


1-22 










37° C. 


h 


None 


+ 


3-96 












h 


+ £ 


+ 


1T7 












£ 


None 


- 


2'7 












£ 


+ h 


- 


4-72 












£ 


-h 


- 


5-12 










h = 59-6 


h 


None 


+ 


4-58 


July 23 
h= 120-4 


h 


None 


+ 6-25 


£ = 1282 


h 


£ 


+ 


0*49 


£ = 1282 


h 


£ 


+ 2-43 


37° C. 


t 


None 


- 


5-88 


160° C. 


£ 


None 


- 5-73 




£ 


h 


- 


10T1 




£ 


h 


- 10-83 




£ 


None 


- 


5-09 










h = 59-6 


h 


None 


+ 


3-76 


ft = 120-4 


h 


None 


+ 6-83 


£ = 2156 


h 


£ 


+ 


0-36 


£ = 2095 


h 


£ 


+ 0-52 


37° C. 


£ 


None 


- 


7-84 


160° C. 


£ 


None 


- 7-97 




£ 


h 


- 


11-51 




£ 


h 


- 13-9 


k = 59’6 


h 


None 


+ 


3-79 


7i= 120 


h 


None 


+ 6-24 


£ = 3781 


h 


£ 


+ 


0-04 


I £ = 3796 


h 


£ 


+ 0-09 


37° C. 


t 


None 


— 


8-98 


160° C. 


t 


None 


- 9-41 




£ 


h 


— 


12*46 




£ 


h 


-15-8 



268 



Proceedings of the Koyal Society of Edinburgh. [Sess. 



Steel. 



Date, 

Fields, 

Temp. 


Cyclic 

Field. 


Steady 

Field. 


Resistance 

Change. 


Date, 

Fields, 

Temp. 


Cyclic 

Field. 


Steady 

Field. 


Resistance 

Change. 


July 26 


h 


None 


+ 2*84 


July 25 


h 


None 


+ 5-15 


h = 53-7 


h 


£ 


+ 0-30 


h— 104 


h 


£ 


-1- 0-86 


£ = 864 


£ 


None 


- 4*59 


£ = 843 


£ 


None 


- 4-44 


34° C. 


£ 


h 


— 7'55 


70° C. 


£ 


h 


- 10-34 


h= 53-7 


h 


None 


+ 2-72 


h = 104 


h 


None 


+ 5-19 


£ = 1282 


h 


£ 


+ o-io 


£ = 1268 


h 


£ 


+ 0-31 


34° C. 


£ 


None 


- 5 53 


70° C. 


£ 


None 


- 5-64 




£ 


h 


- 9-12 




£ 


h 


-11-39 


h = 53-7 


h 


None 


+ 2-77 


h = 104 


h 


None 


+ 5-29 


£ = 2141 


h 


£ 


+ 009 


£ = 2111 


h 


£ 


+ 0-29 


34° C. 


£ 


None 


- 6-29 


70° C. 


£ 


None 


- 6-31 




£ 


h 


- 9-86 




£ 


h 


-12-25 


h = 53-7 


h 


None 


+ 2-89 


h= 104 


h 


None 


+ 4-75 


£ = 3781 


h 


£ 


+ o-oi 


£ = 3706 


h 


£ 


+ 0-22 


34° C. 


£ 


None 


- 7-05 


70° C. 


£ 


None 


- 6-73 




£ 


h 


- 10*73 




£ 


h 


-12-4 


July 29-30 
















h= 158 


h 


None 


+ 6-47 










£ = 606 


h 


£ 


+ 3-12 










160° C. 


t 


None 


- 3-99 












£ 


h 


- 7-75 










h= 156 


h 


None 


+ 669 










£=1268 


h 


£ 


+ 1-08 










160° C. 


£ 


None 


- 5-91 












£ 


h 


-12-53 










h= 156 


h 


None 


+ 6-45 










£ = 3706 


h 


£ 


+ 0-50 










160° C. 


£ 


None 


- 6-77 












£ 


h 


-14-3 











REFERENCES. 

(1) C. G. Knott, “Changes of Electrical Resistance accompanying Longitudinal 
and Transverse Magnetizations in Nickel,” Proc. R.S.E., xxxiii, p. 200 (1913). 

(2) L. Grunmach, “Uber den Einfluss transversaler Magnetisierung auf die 
electrische Leitungsfahigkeit der Metatle,” Ann. d. PhysiJc , vol. xxii, p. 141, 1906. 

(3) W. Morris Jones, B.Sc., and J. E. Malam, “The Electrical Resistance of 
Nickel in Magnetic Fields,” Phil. Mag., April 1914. 

(4) C. G. Knott, “Magnetization and Resistance of Nickel at High Tempera- 
tures,” Part 2, 1906, Trans. R.S.E., xlv, p. 547. 

(5) G. Rossi, “Variazioni di resistenza del mercurio e delle amalgame di bismuto 
nel campo magnetico.” 11 Nuovo Cimento, 1911, serie vi, tomo ii. 



( Issued separately December 14, 1914 ) 



1913-14.] 



Obituary Notices. 



269 



OBITUARY NOTICES. 



Dr A. C. L. G-. Giinther, M.A., Ph.D., M.D., LL.D., F.R.S., etc. 

By William C. MTntosh. 

(Read June 15, 1914.) 

The death of Dr Albert Charles Lewis Gotthilf Giinther, who was elected 
to the Honorary Fellowship of this Society in 1895, has deprived science of 
the most distinguished ichthyologist of his day, and one whose labours in 
other departments of zoology were no less noteworthy. He was born in 
Esslingen in South Germany on the 3rd October 1830, his father being 
“ Siftungs-Commissar ” in Esslingen and “ Estates-Bursar ” in Mohringen, 
a descendant of a family which had been known in the locality for hundreds 
of years — indeed the Swabian branch of the Gunther family was settled in 
and about Mohringen on the Filder Plateau at the beginning of the fifteenth 
century. His mother was Eleonora Nagel, whose family originally came 
from Bremen. Albert was the eldest son, and was sent for his early 
education to the Gymnasium at Stuttgart (1837-47); and subsequently he 
studied at the Universities of Tubingen (1847-52, 1856-57), Berlin (1853), 
and Bonn (1854-55), thus gaining a wide experience of University life and 
a breadth of culture which had an important influence on his future career. 
Descended from a line of clergymen, family tradition destined him for the 
ministry of the Lutheran Church, for which, indeed, he was trained at the 
Theological College of Tubingen, and for which he passed the qualifying 
examination. His natural bent, however, was wholly in another direction, 
and, after taking the degree of Ph.D. in 1852, he decided to study science 
and medicine, taking the degree of M.D. at the same University in 1862. 
Before this, however, he had chosen zoology as the field of his labours, and 
had published his first paper on a Distome as well as a treatise on Fische des 
Neckars, with the coloured figure of a form new to the river (1853), and a 
Randbuch der medicinischen Zoologie (1858). Visiting England in 1855, he 
met Sir Richard Owen and Dr John Edward Gray, who had been interested in 
the former work, and a friendship sprang up between them — resulting in the 
selection of Dr Giinther, in October 1857, to arrange and describe the Fishes, 
Amphibians, and Reptiles in the British Museum ; as well as to prepare 



270 



Proceedings of the Royal Society of Edinburgh. [Sess. 

catalogues of the greater part of the collections. Thus settled with definite 
work before him, and amidst congenial surroundings, Dr Gunther laboured 
incessantly at his great task ; and though the apartments, which were cellar- 
like, in the old Museum in Bloomsbury were far less cheerful than in the 
New Natural History Museum at South Kensington, yet his interest and 
energy never flagged. From the first the Fishes, Batrachians, and Reptiles 
were prominent in his studies, though Birds and Mammals also received 
due attention, as shown in various papers to the Zoological Society. Thus 
his work in the latter group ranged from monkeys, carnivores, rodents, and 
ungulates to marsupials, and from diverse parts of the globe. Besides 
accounts of recent birds, he, along with Mr Newton, investigated the extinct 
birds of Rodriguez. Only a lifelong experience, rigid accuracy, and great 
natural ability could have enabled him to grasp the salient points of forms 
pertaining to such diverse types, and this not in single species, but often in 
hundreds, and whose close resemblances or intricacies of structure were in 
themselves sources of perplexity. 

The extraordinary activity with which he laboured is demonstrated by 
the long list of his works, memoirs, and papers on all the groups mentioned. 
Amongst the more important are such as The Geographical Distribution 
of Reptiles (1858), in which he had forestalled many interesting features 
subsequently described by others ; the memoir on Ceratodus, the lung-fish 
of the Burnett and Mary rivers of Queensland ; that on the structure of 
Hatteria (Sphenodon) from New Zealand; “ On the Giant Tortoises”; and 
the vast array of papers on the Fishes, Amphibians, Reptiles, and occasion- 
ally Birds and Mammals, of every important British expedition, as well as 
collections from every quarter of the globe — from Pole to Pole, and from 
river, lake, sea, and land. The mere perusal of the titles of his papers is no 
light task, whilst every one is the record of a painstaking, laborious research. 
Mr E. A. Smith, one of his colleagues, estimates that, besides the works and 
larger memoirs, there were about 300 papers published in the Journals of 
the London Societies, and that the whole of his writings occupy about ten 
thousand pages, illustrated by a very large number of fine plates and 
text-figures. It is a record remarkable alike for its unswerving devotion 
and notable results, and affords a splendid example to younger men. He 
accomplished much of this work when burdened with the cares of adminis- 
tration, preparing official reports “ in connection with individual members 
of the staff, monthly and annual reports of progress and work accomplished, 
the supervision and editing of catalogues and guides issued by his depart- 
ment, besides the consideration of all proposed acquisitions ” * and the con- 
* E. A. Smith, Zoologist , March 1914, p. 115. 



1913-14.] Obituary Notices. 271 

tinual correspondence. Moreover, to his fellow- workers, such as Charles 
Darwin and A. Russel Wallace, he was of much service in the chapters on 
the distribution and classification of Fishes, Amphibians, and Reptiles. 

The memoir on Geratodus in the Philosophical Transactions is one of 
special interest, as it details the structure and relationship of a Dipnoan 
fish, the ancestors of which were separated by the long gap between the 
present and the Devonian and Carboniferous periods. Yet the persistence 
of type, as pointed out by Dr Gunther, is most remarkable. Further, those 
early representatives were not the beginners of a series, “ but the last of 
many preceding developmental stages.” 

His labours in the British Museum resulted in the issue of eight volumes 
of the Catalogue of the Fishes, a work of immense research, patient in- 
vestigation, and accurate description. In this work (4000 pages) he pays 
a tribute to Johannes Muller’s ordinal arrangement, though he was not 
satisfied that the coalesced pharyngeal bones are of sufficient importance to 
unite the Acanthopterygii and Malacopterygii into one order. An idea of 
the vast labour spent on this task may be obtained by glancing at the 
number of species dealt with, no less than 6843 being well established, 
whilst 1682 others are doubtful. The carrying out of this gigantic task in 
the cellars of the old British Museum in Bloomsbury shows the indomitable 
energy of the investigator as well as his thorough grasp of the subject. It 
is indeed doubtful if such a task will ever again be attempted on the same 
lines, at least without the physical collapse of the investigator. Two 
volumes of a Catalogue of Batrachia salientia and Colubrine snakes 
complete the series of ten volumes. Moreover, the Ray Society published 
his fine work, with numerous illustrations by Ford, on the Reptiles of British 
India. His daily work in the British Museum ranged over snakes from 
West Africa and South America to those from Siam and Australia ; fishes 
from the most recent British dredging expeditions, those from fresh waters 
in every quarter of the globe, and from the neighbouring seas ; amphibians 
from widely distant regions ; birds and mammals from diverse localities, 
and often of great interest. Amongst his other works are the Challenger 
volumes on the shore and deep-water fishes collected in the great expedition. 
The subject of the deep-sea fishes had long been of special interest to 
Dr Gunther, and we may imagine the delight he felt in the study of no 
less than 266 species belonging to this category— many of weird form, with 
remarkable sensory appendages and phosphorescent organs. As he himself 
has stated, the Challenger series laid a broad and sure foundation to our 
knowledge of the abyssal fish-fauna, and he incorporated all the most 
recent work of the Norwegian, American French, and British investigators 



272 



Proceedings of the Royal Society of Edinburgh. [Sess. 



of the deep sea. In the introduction to this fine treatise his experienced 
remarks on phosphorescence and on the nature and distribution of deep-sea 
fishes are of great value and interest. This volume is illustrated by no less 
than 72 plates, many of them double, and admirably drawn by Mintern 
Bros., the successors of G. H. Ford. 

His report on the shore fishes collected by the Challenger was 
published before the preceding treatise, and comprised an account of 1400 
species, of which 94 were new to science. Only a skilled ichthyologist 
could thus have worked out the collection with such rapidity, for it was 
issued in 1886, when Sir Wyville Thomson was still at the head of affairs. 
Rare forms from the tropical Atlantic, Bermuda, the temperate zone of 
the South Atlantic, of the Antarctic Ocean, the temperate zone of the 
South Pacific, of Japan, and the neighbouring regions were accurately 
described and figured. This and the foregoing volume would alone have 
made a reputation. Moreover, it gave Dr Gunther an opportunity of 
widening our views with regard to the mutual relations of the fishes of 
deep and shallow water, and of demonstrating the wide range of many 
forms both in depth and locality. 

One of his greatest services to the science of zoology as a whole, and one in 
which his work has directly proved a boon to all his fellow- workers, is the 
Record of Zoological Literature , which he founded in 1867 and edited for 
several years. Investigators have thus a ready means of making themselves 
acquainted with contemporary work in every country. This step alone 
would have earned the thanks of every zoologist, and its continuance to-day 
by the Zoological Society shows its permanent importance. The work must 
have given Dr Gunther much thoughtful labour and care, and could only 
have been undertaken by one in a central position, and with the co-operation 
of a wide circle of zoological friends at home and abroad. 

His Introduction to the Study of Fishes (1880) is another treatise 
which has had a widespread popularity — from the masterly way in which 
the author handled a subject to which he had devoted the best part of 
his life. No student of the group can find a more comprehensive yet 
concise treatise in any language, and none having an equal amount of 
reliable information. His chapters on the distribution of fishes — geological 
and geographical — are especially full of experienced remarks. 

Though Dr Gunther in his early days made a few of his own drawings, 
he soon became so occupied that it was necessary to employ others, and 
he was fortunate in securing for many years the services of G. H. Ford — 
who was facile princeps in lithography during his day, and who in the 
delineation of the lower vertebrata has never been surpassed — and he 



1913-14.] Obituary Notices. 273 

acquired a special skill in illustrating the memoirs of Dr Giinther, whose 
appreciation of a fine drawing was ever forthcoming. 

Entering the British Museum in 1857, he by and by was appointed on 
the staff, and he rose step by step till in 1875 he became Keeper of the 
Zoological Department in succession to his friend Dr J. E. Gray, and he 
held this post for twenty years. His record in this institution is remark- 
able — as beneficial to the Museum as creditable to himself. His catalogues 
have already been alluded to, and the vast array of original contributions 
to the Royal, Zoological, and Linnean Societies formed an unbroken 
succession from first to last. The latter alone would have made a great 
reputation, yet they were but fragments of his daily work in perfecting 
the numerous collections committed to his care, in carrying out the 
endless duties of administration, and in devising improvements. More- 
over, the construction of the New Natural History Museum at South 
Kensington, the scheme of Sir Richard Owen, likewise gave him increased 
responsibilities in connection with the arrangement of the galleries and 
cases, and still more with the transfer of the vast and valuable collections 
to their new premises. This task, perhaps, brought out the administrative 
talents and practical skill of the Keeper of the Department more promi- 
nently than anything else, and well merited the special minute of the 
Trustees on its successful completion. Amidst the array of vans, lorries, 
cabs, and conveyance by hand, no specimen of value was lost or broken. 
Nor was the rearrangement in the new Museum less successfully carried 
out, though not a few serious obstacles were encountered. Thus when the 
cases for the mammals on the ground floor were being arranged, it was 
found that the architect’s ornamental projections on the walls were inimical 
to satisfactory adjustment, and thus this Class had to be placed on the 
first floor. He also insisted on the advantages of a separate building for 
specimens preserved in spirit, both for the greater safety of the extensive 
collections in jars, and for the security of the other portions of the 
magnificent building. 

Some idea of the extent of the National Collection may be gained when 
it is mentioned that in 1880 there were 1,300,000 zoological specimens, 
and that when Dr Gunther retired in 1895 there were 2,245,000. Known 
all over the world for his labours in zoology, and having an extensive 
acquaintance with naturalists and travellers, much of this progress was 
due to his tact and personal influence — and, it may be added, to his personal 
example, for from his earliest days he was a field-naturalist as well as 
a scientific author, and he never missed an opportunity of adding to the 

collections in the British Museum, whether as the result of his own 
VOL. xxxiv. 18 



274 Proceedings of the Royal Society of Edinburgh. [Sess. 

dredging and collecting expeditions, or by securing from friends such rare 
forms, for example, as Leptocephali. 

In connection with the fittings of the National Collection at South 
Kensington, it is also interesting to remember that he favoured the con- 
struction of metal cases instead of wood, though the Government did not 
adopt this plan — probably on the score of expense. He was indeed one of 
the earliest in this country to show the advantages of such cases now fitted 
up in the most advanced museums. Further, from an early period of his 
career in the Museum he saw the importance of having a reference library in 
addition to a general library in connection with the Zoological Department, 
and he persistently exerted himself to carry out this aim. The severance 
of the collections from the proximity of the great library in Bloomsbury 
made this the more necessary, and now the New National History Museum 
has an important and invaluable general as well as a special zoological 
library — an inestimable boon to visiting naturalists as well as to the staff. 

Yet another side of Dr Gunther’s services in the British Museum merits 
attention, viz. the development of the systematic work in the Museum. 
Thus he succeeded in increasing the scientific staff gradually from 4 to 13, 
and by a skilful modification of the duties of the attendants he managed 
to relieve the trained men from menial duties and enlist their services 
in highly skilled museum-work. Thus the scientific staff had at their 
disposal a body of experienced and reliable practical aids, so that their 
progress was rendered both rapid and satisfactory. 

His services as a Vice-President of the Royal and Zoological Societies, 
and President of the Linnean Society, must have entailed a large absorp- 
tion of his time and energies — especially as many of his memoirs and 
papers were communicated to one or other. 

It might be supposed that one so constantly and so actively engaged 
in the pursuit of science had little time for attending to the interests of 
visitors to the collection. Yet, if he had done nothing more than in- 
augurated the fascinating and instructive cases containing the nesting 
of birds as now exhibited in the Museum, such would have been memor- 
able. No feature in the great collection is more popular than these life- 
like illustrations of the British nesting birds of both sexes, their eggs, 
newly hatched young, and their environment. As he himself has stated, 
it was essential that the actual birds which made the nest, with their 
eggs or young, should be secured, and the surroundings taken from the 
spot, the only artificial elements being flowers, leaves, or structures which 
could not be preserved satisfactorily. In the case of such birds as the 
bustard and the ruff, the remarkable plumage and attitudes of the males 



1913-14,] Obituary Notices. 275 

form an additional attraction in these charming scenes. None but a 
skilful field -naturalist in whose mind the actual scenes had imprinted 
themselves could have designed these wonderful cases ; and Dr Gunther 
has often said that he gained as much real knowledge from Nature as from 
the splendid libraries at his command. 

His work in the other departments, viz. Mammals and Birds, was no less 
noteworthy. Every important and unimportant expedition consigned to 
him the fishes, amphibians, and reptiles, and occasionally the birds and 
mammals, and his conscientious treatment of them was uniformly the 
same, whilst his personal influence with the collectors was a constant 
source of rich additions to the National Museum. 

By Dr Gunther’s recommendation many valuable collections were added 
to the British Museum, such as the Gould Collection of Birds, the Oates 
Collection of the Birds of Pegu, Goodwin- Austin’s Indian Birds, the Sclater 
Collection of Birds, Capt. Shelley’s African Birds, the Saville-Kent Corals, 
the Baly Collection of Phytophaga, the Bates Collection of Heteromera, 
the Zeller Lepidoptera, the Keyserling Arachnida, the Moore Indian Lepido- 
ptera, the Pascoe Coleoptera, the Morelet Land and Freshwater Shells, the 
Atkinson Coleoptera and Rhynehota, the Grote North American Lepido- 
ptera, and the Parke Foraminifera. 

His great knowledge of zoology and ichthyology in particular, as 
well as his familiarity with the habits of animals, caused his services to be 
much sought after by Government Commissions and municipal bodies in 
regard to their fresh waters. Thus he reported on the pollution of the 
Thames and on that of several trout and salmon rivers. His evidence on 
the pollution of the Lower Thames was of great importance as well as 
conclusive, for his careful experiments proved the effects of such on fishes, 
and he indicated the length of time they would survive in various kinds of 
polluted water, e.g. sewage, effluents from gas-works, ink-works, etc. He 
went, for instance, minutely into the question, surveying the Lower Thames 
in a steam- vessel placed at his disposal by the Metropolitan Board of Works, 
and thus was enabled to give reliable advice to that body. His evidence 
in connection with the “ yellow fins” of the Allan Water was another 
example of his acuteness and caution in dealing with a contested point. 

Moreover, Dr Gunther was ever ready to encourage local collections of 
objects of natural history, and his gifts to provincial museums, of tame 
birds for private parks and aviaries, are gratefully remembered. One of 
his last donations was that to the University Museum of St Andrews, to 
which he presented about fifty exquisitely coloured birds, ranging from 
Reeve’s pheasant and the capercaillie to humming-birds, the group of the 



276 Proceedings of the Royal Society of Edinburgh. [Sess. 

Pittas being especially noteworthy for their striking coloration. The 
majority came from the collection of A. Russel Wallace, though some, such 
as the young kestrels, were reared by himself. 

Since he came to England in 1856 he took an interest in the marine 
fauna — indeed in that year a local publication included his contributions 
to the marine fauna of Brighton. His holidays were generally devoted 
to the increase of the Museum’s marine or freshwater fishes and other 
forms. At St Andrews he collected in a day or two various fishes and 
ten species of marine annelids. An excellent sailor, he sometimes was the 
only effective naturalist on board a boat or yacht, as, for example, when 
the distinguished Professor Kolliker of Wurzburg requested his aid off the 
south coast of England. His tanks for the preservation of the large fishes 
always accompanied him in these excursions. None enjoyed the freedom 
of forest, moor, or hill, or the quietude of a river bank more than he, and 
thus he gained an intimate knowledge of Nature — both animate and inani- 
mate — so important for the head of the Zoological Department of the 
National Museum. This knowledge, gained by close observation on the 
Continent of Europe, in Britain, and in the adjoining seas, made him a 
delightful companion, and there were few who were more welcome than he 
at the country-seats both of England and Scotland. Moreover, he was an 
excellent shot — a reminiscence, perhaps, of his military experiences in South 
Germany — and an expert angler. At one time he took an active interest 
in the introduction of the Sheat-fish ( Siluris glanis) to English waters, and 
with success ; but the voracious habits of these large fishes proved disastrous 
to the salmonoids, and the attempt was not repeated. 

Quite lately he prepared for the Trustees a brief account of the changes 
in the British Museum (Natural History) from 1858 to 1895 — that is, during 
the period of his official connection with the institution. The continuous 
stream of important additions, many of which were due to the influence of 
the Keeper himself, the increase of the assistants, the inauguration of 
systematic publications by the staff, the transference of the greatest collec- 
tion of the kind in the world from the old to the new quarters, and the 
introduction of every modern improvement in arrangement, are told with 
the characteristic modesty and restraint of the veteran investigator. 

Dr Gunther was the recipient of many honours both at home and 
abroad. He was a Vice-President of the Royal and Zoological Societies, 
President of the Linnean Society, President of the Biological Section of the 
British Association, and a Fellow of most of the learned societies at home 
and abroad. He was awarded a Royal Medal by the Royal Society, and 
the Gold Medal of the Linnean Society. 



1913-14.] Obituary Notices. 277 

Dr Gtinther had a tall, somewhat lightly-built, wiry physique which 
for nigh sixty years stood without a break the stress and strain of official 
life, the unhealthy atmosphere in the old cellar in the basement at 
Bloomsbury, and the incessant demands of scientific work. His hair was 
fair, eyes blue, and his complexion fresh. Throughout his long period of 
public service, he was never known to have sick-leave. Of strong person- 
ality, and resolute when he had once formed a conclusion, yet he was not 
only an agreeable colleague, but a warm friend to a large circle of acquaint- 
ances. In his home he was one of the kindest parents, ever ready to 
sacrifice himself for the happiness of his family, who had an equally warm 
attachment to him. Of active habit, and delighting in his garden and his 
pets, he was ever busy and cheerful. His first home at Hampton Wick, 
and those subsequently at Surbiton and at Kew Gardens, all reflected the 
tastes of an enthusiastic naturalist whose pleasure lay in everything with 
life. His myrtles and other shrubs and trees at Surbiton, his maiden-hair 
tree and collection of rare shrubs and plants at Kew Gardens, his aviaries, 
house-pets, and his observations on the birds in Kew Gardens, were a 
never-failing source of interest and information to himself and others. 
His health suffered some years ago from a severe attack of pneumonia, but 
lately was satisfactory until an abdominal affection necessitated an opera- 
tion from which he did not rally. He was buried in the quiet cemetery 
at Richmond, mourned by a large circle of scientific friends. 

Dr Gunther was twice married. His first wife, Roberta MTntosh, of 
St Andrews, made the exquisite coloured figures of marine animals, many 
of which have been published by the Ray Society ; their son, Robert, 
is a Fellow and Tutor of Magdalen College, Oxford, and the author of 
various able works and memoirs. Dr Gtinther’s second wife, who, with a 
son, survives him, was Theodora Dowrish Drake, from Cornwall, a lineal 
descendant of a brother of Sir Francis Drake. 

Dr Gtinther will ever be remembered as a great systematic zoologist 
who had early and independently worked out many of the problems of 
the distribution of animals which subsequently were more prominently 
associated with other names, as an original investigator and facile princeps 
in Fishes, Amphibians, and Reptiles, and as a man of untiring energy, re- 
markable power of penetration, and of great administrative capacity. More- 
over, the interests of the public and of scientific workers at home and 
abroad were ever safe in his hands. Nowhere will the results of his life- 
long labours be more keenly appreciated than in the British Museum, the 
distinguished staff of which paid the last tribute to the veteran zoologist 
in the peaceful cemetery at Richmond. 



278 Proceedings of the Royal Society of Edinburgh. [Sess. 



John Sturgeon Mackay, M.A., LL.D. By George Philip, M.A., D.Sc. 

(Read July 6, 1914.) 

The task which the Society has entrusted to me of putting on record some 
suitable memorial of the life and work of Dr John S. Mackay is one which 
I feel honoured in undertaking. At the same time I am conscious of my 
own limitations in attempting to give to the scientific world a biographical 
notice of one who was rightly looked on as one of the most learned men of 
the day, and who possessed all the graces which a well-stored mind can 
bestow, along with those subtle and ingratiating qualities of the heart 
which cast such a magnetic influence on all who were privileged to know 
him. Dr Mackay was, in very truth, the beau ideal of a scholar and a 
gentleman, and death has removed from the circle of his friends one who 
will long be missed. His death took place at his residence, 69 North- 
umberland Street, Edinburgh, on March 25 of this year. 

John Sturgeon Mackay was born at the village of Auchencairn, Kirk- 
cudbrightshire, on October 22, 1843, so that at the time of his death he was 
in his seventy-first year. While he was yet an infant, his parents removed 
to Perth, and there he spent his boyhood and received his early education. 
At Perth Academy he showed that aptitude for learning which later 
brought him great distinction, and it is well to note here that his preliminary 
education laid the foundation of both his linguistic and mathematical 
studies. The biographer of the late Professor Chrystal in the Society’s 
Proceedings makes a similar remark ; so that we have these two con- 
spicuous instances at least of men who combined mathematical with 
classical or linguistic talent. One would fain recall here the advice given 
by Lagrange to Cauchy’s father when consulted by him as to the proper 
education for his boy : “ Do not allow your son to open a mathematical 
book nor to touch a single diagram until he has finished his classical 
studies.” To the end Dr Mackay was a strenuous supporter of the old- 
fashioned classical education, and never ceased to deplore the modern trend 
of early specialisation, holding that preliminary education ought to be 
devoted to the cultivation of all the faculties, and not to the development 
of any one at the expense of the others. 

After a school career that gave great promise of later distinction, 
Dr Mackay proceeded to St Andrews University, where he followed the 



1913-14.] Obituary Notices. 279 

usual course at that time imposed on aspirants to a degree. The highest 
honours in mathematics and classics were won by him, and one of his 
fellow-students, himself a man of eminence, has told me that he was looked 
upon as the ablest man of his year. His original intention on leaving the 
University was to enter the ministry of the United Presbyterian Church, 
and with that in view he attended the Theological Hall in connection with 
that body in Edinburgh. Theology, as it was presented to him fifty 
years ago, was not to his taste, and he decided to renounce his intention of 
qualifying for admission to the Church, and to take up teaching as a 
profession. His first situation was on the mathematical staff of his old 
school, Perth Academy, so that, as he was fond of relating, he had as a 
predecessor William Wallace, afterwards the eminent occupant of the 
Chair of Mathematics in Edinburgh University. His stay in Perth was 
short — two years, 1 think, — and in 1866 he received an appointment as 
mathematical master in Edinburgh Academy, an institution which retained 
his services until he retired in 1904. His long connection with this well- 
known school had far-reaching effects both on the school and on Hr Mackay 
himself. To the very last he took unabated interest in all that pertained 
to the life of the school, and showed the most unswerving loyalty to every- 
thing connected with it. Indeed, at the beginning of the present year, 
when his eyesight failed him, he was engaged in compiling a register of 
pupils who attended the Academy since its establishment in 1824. Many 
of his pupils have risen to great eminence in various walks of life, both at 
home and abroad, and few of them revisited Edinburgh without spending 
some hours with their old master, whom they were proud to reckon among 
their friends. His affection for his pupils was real and genuine, and he 
followed their careers with a truly paternal interest. 

Dr Mackay was singularly well suited for a teacher. His ready sympathy 
and kindly disposition immediately secured for him the goodwill of his 
pupils, while his great learning and nobility of character were so evident 
that they must have exercised a very powerful influence for good on the 
whole school. His well-stored mind was ever ready to give of its contents ; 
and, while some men in such circumstances look on their learning as 
wasted, Dr Mackay, quite otherwise, thought nothing too good for his 
boys. A pupil of his own, a distinguished man of letters of this city, has 
put on record the following appreciation, and I cannot do better than quote 
his words : “ In reviewing the list of those with whom he happens to have 
been brought into contact, the present writer can think of few more richly 
endowed than he with the qualities which really matter. He was eminently 
straight, he was eminently loyal, and he was eminently magnanimous. It 



280 Proceedings of the Royal Society of Edinburgh. [Sess. 

is of less consequence, yet not to be recalled without a pang, that he had 
a delightful sense of humour, which, coupled with the control he possessed 
over his vast stores of learning, rendered him the most charming of com- 
panions. A school may reckon itself fortunate which has inscribed on 
the roll of its masters the name of so learned, so accomplished, and so good 
a man as was John Sturgeon Mackay.” * 

His retirement from active duty dates from 1904, and as he was com- 
paratively vigorous he looked forward to a period of great usefulness. He 
still spent two months or so of the year on the Continent, and also con- 
tinued his mathematical researches. But latterly his intimate friends 
noticed a diminishing vitality, and although he came back every year 
refreshed and invigorated by the change, it was evident that the heavy 
self-imposed strain of many years was now beginning to tell on him. In 
January of this year, failing eyesight was the first indication that things 
were not right; and as this condition grew steadily worse, it became evident 
that it was symptomatic of very serious weakness, and after lingering for 
a few weeks he passed peacefully away on Wednesday, March 25. Having 
his time so fully taken up with more congenial pursuits, Dr Mackay took 
little or no interest in those affairs that bring men prominently into the 
public eye. To his friends he showed a warm and affectionate disposition ; 
stimulating in his criticism but never censorious, he had the happy faculty 
of saying the right thing and doing the right thing at the right time. 
Anything in the nature of sham, morally or intellectually, was specially 
abhorrent to him, and he very readily detected it. But those who showed 
even in a small degree an inclination to do something more than merely 
“ put in the day ” found in him a staunch friend, willing to do his utmost 
in assisting them in their work, and by his kindly and well-directed 
counsel enabling them to bring their labours to a happy issue. His 
reputation for accurate scholarship extended beyond the confines of his 
own country, and he was frequently appealed to for information by 
savants all over the world. Included among his intimate friends were 
such well-known men in the domain of mathematical science as Neuberg, 
d’Ocagne, Laisant, and Aubert in Belgium and France, Moritz Cantor in 
Germany, and Robert Tucker in our own country. 

The Royal Society did him the honour of electing him to a Fellowship 
in the year 1882 ; and although he admitted the prior claims of the Edin- 
burgh Mathematical Society for his support in the matter of original 
papers, he did useful work as a member of the Council and also as a 
member of its Library Committee. By making him an Honorary Fellow 
* See Edinburgh Academy Chronicle for May of this year. 



1913-14.] Obituary Notices. 281 

ten years ago, the Society showed its appreciation of the great service 
Dr Mackay rendered to scientific learning. His extensive knowledge of 
books was recognised by his appointment as a member of the Permanent 
International Bibliographical Association. His alma mater , the Univer- 
sity of St Andrews, readily granted him the highest distinction she could 
offer and in 1884 conferred on him the degree of LL.D. He served two 
periods as Examiner in Mathematics in St Andrews, and for many years 
he occupied a similar position on the Examining Board of the Chartered 
Accountants’ Society of Scotland. He was elected by the Edinburgh 
Mathematical Society as its first President, and it is not the least of his 
claims to our remembrance that he gave such whole-hearted support to 
its affairs that it was a constant pleasure to him to see it grow from a 
small beginning, with a membership of two score, to its present position of 
influence, with a membership of two hundred and fifty scattered over the 
four quarters of the globe. His zeal for the welfare of the Society never 
diminished, and until within the last few years, when his health began to 
decline, he was seldom absent from its meetings. As was to be expected 
from such an accomplished French scholar as he was, he took a very 
prominent part in the work of the Franco-Scottish Society, and attended 
several of its excursions through France. 

In giving an account of the scientific work of the late Dr Mackay, it 
will be simplest to deal with it in the historical order of its development. 
At the outset, it is no exaggeration to say that the whole domain of pure 
geometry, in so far as it deals with plane figures, came under his notice, and 
a list of his published papers will show that he enriched almost every part 
of the subject by discoveries of more or less importance. A very prominent 
place must be assigned to his knowledge of Greek geometry. His great 
command over Latin and Greek made him singularly well qualified to deal 
with this fascinating subject, and only a mere chapter of accidents prevented 
him from obtaining the full honour to which his labours entitled him. 
The seventeenth- and eighteenth-century geometers like Commandinus, 
Edmund Halley, and Robert Simson had studied and edited, as far as they 
could, the works of Archimedes, Apollonius, Euclid, and Diophantos, and 
fairly complete collections of the works of these mathematicians were 
available ; but very little attention had been paid to the writings of Pappus, 
one of the latest of the Alexandrian school of mathematicians. Dr Mackay 
made up his mind to supply the defect, and for many years he spent his 
vacations working patiently and laboriously at the MSS. of Pappus in the 
British Museum and in the Continental libraries, collating and translating 
them. He had practically finished his task, when Hultsch, the celebrated 



282 



Proceedings of the Royal Society of Edinburgh. [Sess. 

German commentator, published his three-volume edition of Pappus, and 
Dr Mackay took no further steps to bring his out. This is all the more 
regrettable as British scholarship could well have stood a native edition of 
Pappus ; and although Dr Mackay very magnanimously admitted that his 
Pappus was in no way superior to that of Hultsch, it is not to be doubted 
but that mathematical literature would have been greatly richer to-day if 
his book had been published. I understand that Sir T. L. Heath is soon 
to add Pappus’ “ Mathematical Collections ” to his excellent editions of 
Archimedes, Apollonius, Diophantos, and Euclid, and so remove the stigma 
that English mathematicians are no longer interested in Greek mathematics. 
Dr Mackay was unfortunate, too, in coming so soon after Allman, whose 
researches in Greek geometry appeared first in Hermathena and afterwards 
in book form. These circumstances to a certain extent robbed him of the 
full honour due to his original work, but, nevertheless, he was looked upon 
as one of the foremost living authorities on Greek mathematics. His 
reviews of Heath’s Diophantos and of Gow’s History of Greek Mathematics 
in the Academy give us an insight into his grasp of the subject, and 
make us regret all the more that we have not a work from his own pen 
dealing with the early history of geometry. He was par excellence the 
man to have done it. 

These studies naturally led on to the work of the Scottish geometers, 
Robert Simson and Matthew Stewart, who were more Euclid than Euclid 
himself in their methods of geometrical analysis, and Dr Mackay subjected 
their works to a most exhaustive examination. To mention only one of 
the results that followed from this, I might note that he finally settled the 
question as to who was the original discoverer of the so-called Simson Line, 
and he showed that Robert Simson has no claim to that honour, but that 
the theorem in question is due to William Wallace, who published it under 
a nom de plume in the Mathematical Repository (old series), ii, 111.* 
Popular periodicals of the type of the Repository , the Lady's and Gentle- 
man's Diary, etc., were forms of mathematical literature that flourished 
in our country from the middle of the eighteenth to the middle of the nine- 
teenth century, and were supported very greatly by non-academic mathe- 
maticians. These journals gave incontestable proof that mathematical 
science, and particularly geometry, was very widely studied in our country, 
and was a source of pleasure and amusement to many whose daily avoca- 
tions required physical rather than intellectual energy. Many of the 
problems dealt with were of a high order, and afterwards formed a 
prominent part of geometrical science. The existence of the nine-point 
* See Dr Mackay’s paper in Edin. Math . Soc. Proc ., vol. ix. 



1913-14.] Obituary Notices. 283 

circle, properties of symmedians and symmedian points, etc., were early 
discussed in the diaries. Dr Mackay made a close study of these journals, 
and the results of his labours were communicated to the French 
Association for the Advancement of Science at their Congress at Besangon 
in 1893, in a paper entitled “ Notice sur le journalisme mathematique en 
Angleterre.” 

Dr Mackay ’s original papers were practically all published in the 
Proceedings of the Edinburgh Mathematical Society, and they constitute 
the most valuable record in our language of the geometry of the triangle. 
It is quite impossible to give here even the titles of all his papers, but 
it may be stated that no earnest student of any branch of plane geo- 
metry can afford to neglect his writings.* They deal with the nine-point 
circle, the six scribed circles of a triangle, isogonals, symmedians, and 
isogonic centres of a triangle. Perhaps his most valuable contributions 
are “ The Triangle and its Six Scribed Circles,” published in vol. i, vol. ii, 
and vol. xi of the above Proceedings , and “ The Symmedians of a Triangle 
and their Concomitant Circles,” in vol. xiv. The first of these two occupied 
several years of his leisure, and to make it as complete as possible he enlisted 
the services of such well-known geometers as Tucker, Neuberg, Fuhrmann, 
and d’Ocagne. We may judge of the completeness of the work when we 
know that it occupied 1600 quarto pages of MS. His paper on the 
“ Symmedians of a Triangle ” made known for the first time in an English 
journal the remarkable properties of the K points and of the Tucker 
group of circles which have as particular cases the first and second 
Lemoine circles, the Taylor circle, and the Adams’s circle. 

Dr Mackay was also the author of the articles “ Calendar ” and 
“ Geometry ” in Chambers’s Encyclopaedia, and “ Euclid ” in Encyclopaedia 
Britannica. The interesting and learned article on “ Numeration ” in the 
jubilee volume of the Chartered Accountants’ Association of Scotland is 
also from his pen. 

Of his books the most important is his Elements of Euclid (W. & R. 
Chambers, Edinburgh, 1884). Like many others, it is based on the well- 
known edition of Robert Sim son, but it shows a vast improvement on 
any previous text-book. Every page of it shows evidence of ripe scholar- 
ship, and it possesses what no other text-book we know possesses, viz. 
references to original memoirs and authorities and full historical notes. 
Writers of mathematical text-books in general carefully avoid introducing 
such personal elements, and thereby in our view make a very great 

* A list of these papers will be found in the index volume of the Edinburgh Mathe- 
matical Society. 



284 



Proceedings of the Royal Society of Edinburgh. [Sess. 

mistake. The idea that the subject has reached its present condition by 
the labours of many workers, largely obscure, is very helpful to learners, 
and gives a humanistic trend to the study of geometry. A Key to the 
Elements was published in 1885. 

It is almost needless to say that Dr Mackay did not view with favour 
the departure from the Euclidean sequence. He held that some logical 
sequence is necessary, and that Euclid’s is superior to any more recent 
innovations. Signs are not wanting that his views are now being shared 
by a growing number of mathematicians, who detect in our present 
system too much looseness and slovenliness. He was requested to write 
a text-book of geometry in accordance with the recent movement ; and 
although he complied with the request and produced his Plane Geometry , 
books i-iii in 1904, and books iv-v in 1905, they naturally have not 
the characteristic features of the earlier work. His Arithmetic Theoretical 
and Practical appeared in 1899, and forms one of the soundest and 
most illuminating books we have on the subject. 

This short account of his work will show the great service Dr Mackay 
rendered to mathematical learning, and the loss the scientific world has 
sustained by his death. 



1913 - 14 .] 



Obituary Notices. 



285 



Professor John Gibson. By Principal A. P. Laurie, D.Sc. 

(MS. received October 26, 1914. Read December 7, 1914.) 

John Gibson was born in Edinburgh on May 13, 1855, and was educated 
at Edinburgh Academy. He afterwards studied chemistry at Heidelberg 
under Bunsen, Kirchhoff, Kopp, and others, working for five consecutive 
sessions in Bunsen’s laboratory, and graduating in 1876 as Doctor of 
Philosophy. 

On returning to Edinburgh, he became assistant under Professor Crum 
Brown; later on, in 1881, being appointed chief assistant in the laboratory, 
where he taught for eleven years. In 1892 he was appointed Professor of 
Chemistry in the Pleriot-Watt College, a post which he held up to the day 
of his death. 

Gibson was, above all things, an analyst. He seems to have developed 
his original interest in chemical analysis under Bunsen, and to the end of 
his life he remained in the very first rank of analysts, and always regarded 
that part of the teaching in the department as of the utmost importance. 

As an example of his capacity for analytical research, we cannot do 
better than take his report on “ An Analytical Examination of Manganese 
Nodules, with special reference to the Presence or Absence of the Rarer 
Elements,” which was published in the Challenger Reports — “ Deep Sea 
Deposits,” in 1891, and involved an original research in analytical methods. 
All those who had the good fortune to be students under him have benefited 
by his enthusiastic appreciation for, and exact knowledge of, analytical 
methods. 

While in Edinburgh University, Gibson carried out a large number of 
observations for the Fishery Board on the composition of sea waters, more 
especially in the North Sea, and he also made an investigation into some 
of the rare earths. Years of investigation were devoted to the study of 
these rare earths, and the separation of pure salts from them. Unfor- 
tunately, all that ever was published on this subject was a short paper on 
“ Glucinum ” in the Transactions of the Chemical Society, 1893. 

Gibson always approached the problem of publication with great un- 
willingness. When once he completed a research, his interest carried him 
on to fresh investigations, and it was with great difficulty that he could be 
persuaded to put pen to paper with a view to publication. As a conse- 
quence of this, many valuable researches have been lost to science, and this 



286 Proceedings of the Royal Society of Edinburgh. [Sess. 

is especially the case in connection with glucinum, cerium, lanthanum, and 
didymium. Large quantities of the minerals were worked up, pure salts 
prepared, and much work was done, which has no doubt since been con- 
firmed by others, although it may be questioned whether even now all 
Gibson’s results have been re-established. 

About the time when the paper on glucinum was published, Gibson 
started some experiments on the effects of light on such changes as the 
conversion of chlorine water into hydrochloric acid, the resulting observa- 
tions being published in a short paper on “ Photochemical Action ” in the 
Proceedings of the Royal Society of Edinburgh in February 1897. This 
was followed by a short paper, “ A Preliminary Note on a Characteristic of 
Certain Chemical Reactions ” ( Proc . Boy. Soc. Edin., Dec. 1897). The origin 
of these papers was as follows : In studying the action of light on these 
mixtures, Gibson discovered the fact that the amount of change depended 
on whether the final result of the reaction was to increase the electrical 
conductivity of the solution as a whole or to diminish it, there being a 
tendency for any such solution to move in the direction of increased 
electrical conductivity. This led him further to investigate the question as 
to how far other reactions, apart from those caused by light, were influenced 
by these conditions. 

No particular physical value had been, so far, associated with the 
electrical conductivity of a system as a whole, and the whole direction of 
research was proceeding towards experiments on very dilute solutions, 
with a view to the application of the laws laid down by van’t Hoff, 
Arrhenius, Kohlrausch, and Nernst to the problems of electrochemistry. 
It was probably for this reason that more attention has not been directed 
to the very interesting results obtained by Gibson in this direction. 

In the preliminary paper already referred to he gives examples of the 
law that many chemical reactions are governed by the tendency of a 
solution to develop a state of maximum conductivity in the system, these 
examples being : the dehydration by hydrochloric acid of hydrated 
cobaltous chloride ; the dehydration of sugar by sulphuric acid ; the re- 
duction of chromic anhydride by hydrochloric acid ; the oxidation of 
hydrogen iodide by sulphuric acid ; and the oxidation of nitric oxide by 
nitric acid. 

In order to carry these investigations further, he decided to redetermine 
the conductivity curves of some of the best known acids and salts, and 
devoted a great deal of time and labour to these measurements, with the 
result that there can be no doubt that the most exact conductivity curves 
that we have for hydriodic, hydrobromic, and hydrochloric acids, and 



1913-14.] Obituary Notices. 287 

ammonium bromide, lithium bromide, and sodium bromide, are those 
determined by Gibson ; whilst for these experiments he devised his 
electrically controlled thermostat, which is a very perfect instrument 
of its kind. 

The main interest of his work, however, remains as before the study of 
the relation between maximum conductivity and certain types of chemical 
change. He showed, for instance, the close relation between this and the 
precipitation of salts from solution by hydrochloric acid ; the behaviour of 
aqueous solutions of hydrogen chloride towards dissolved oxygen and 
dissolved chlorine respectively; the oxidation of hydrogen chloride in 
aqueous solution by chromic acid ; the action of hydrochloric acid as an 
esterifying agent ; and the action of hydrogen chloride on acetal- 
dehyde, aldol, and crotonaldehyde, and of hydrochloric acid on cobalt 
chloride. In addition, he investigated the decomposition of aqueous solu- 
tions of hydrogen iodide ; the behaviour of nitric acid when exposed to 
light ; and, in more detail, the action of sulphuric acid on sucrose and on 
formic acid. In all these cases he proved quite definitely that the limit to 
which the reaction was carried was fixed by the point at which the system 
as a whole reached its maximum conductivity, and that many reactions 
were reversed on each side of this maximum conductivity point, proceeding 
in opposite directions when once the maximum of the curve had been 
passed. 

It is, of course, evident that there are a large number of reactions which 
are not governed by this condition, and this is one of the reasons why for 
many years Gibson hesitated to publish his results, as he wished to get 
some definite law by which he could distinguish between reactions which 
were governed by the maximum conductivity and those that were not. 

It is probably safe to say from his results that all chemical systems 
which are electrolytes tend towards the point of maximum conductivity, 
although there may be other forces at work which are sufficiently powerful 
to conceal this tendency ; but whenever we are dealing with balanced 
reactions in which a very small change of conditions will make the re- 
action proceed the other way, we find the maximum conductivity of the 
system is the governing condition. There can be no doubt that we have 
therefore to look for the widest application of this principle when dealing 
with plant and animal life, where we have such a delicate balance constantly 
occurring between two possible directions of chemical change. 

Gibson has shown the application of his theory to the change from 
sugar to starch, and again from starch to sugar, in the leaf of the plant, 
and he also made a considerable number of experiments — which, un- 



288 



Proceedings of the Royal Society of Edinburgh. [Sess. 

fortunately, will now never be published — on the influence on enzymatic 
reactions of the same condition. His experiments on mustard powder and 
on crushed bitter almonds have already been published in the paper 
on “ The Significance of Maximum Specific Electrical Conductivity in 
Chemistry” {Trans. Roy. Soc. Edinburgh, xlviii, Part I, No. 6). These 
will be found well worthy of study by those who are interested in plant 
chemistry and in enzymatic changes. It is certainly open to question 
whether one of the controlling conditions of enzymatic reactions will not 
be found to be the nature of the mineral salts that are present, and the 
amount of dilution or concentration required to bring the solution of the 
salt to its maximum conductivity point. 

John Gibson was elected a Fellow of the Royal Society of Edinburgh 
in 1877, and twice served as a member of Council, from 1892 to 1894 and 
from 1897 to 1900. He was of great service to the Council when papers 
of a chemical nature were under consideration. 

Gibson had just completed the fitting up of the new laboratories at the 
Heriot-Watt College, and had only entered into possession of them for a 
couple of months, when his death occurred, on January 1, 1914. 

It was a peculiarly hard stroke of fate that he should not have had 
the opportunity of enjoying for a longer time those laboratories in which 
he had taken so great an interest, and to the completion of which he had 
for so long; looked forward. 

The following is a list of his papers published in the Society’s Pro- 
ceedings and Transactions : — 

In the Proceedings, R.S.E. 

1. On some Laboratory Arrangements. April 2, 1883. Yol. xii. 

2. On Peroxides of Zinc, Cadmium, Magnesium, and Aluminium (with 
R. M. Morrison). Read July 5, 1880 : published 1885 in vol. xiii. 

3. On Papers by MM. Haas, Cleve, and Lecoy de Boisbaudran, on the 
Production of Peroxides by means of Peroxide of Hydrogen. April 6, 
1885. Yol. xiii. 

4. The Action of Sodium Carbonate and Bromine on Solutions of 
Cobalt and Nickel Salts. February 17, 1890. {Abstract.) Yol. xvii. 

5. Manganese Deposits in Marine Muds (along wdth R. Irvine). 
January 9, 1891. Yol. xviii. 

6. On the Chemical Composition of Sea-water. July 3, 1893. Yol. xx. 

7. On Photo-chemical Action. February 15, 1897. Yol. xxi. 

8. Preliminary Note on a Characteristic of Certain Chemical Reactions. 
December 6, 1897. Yol. xxii. 



1913-14.] Obituary Notices. 289 

9. On a Thermostat electrically heated and regulated (Title only). 
February 5, 1900. Yol. xxiii. 

10. On certain Relations between the Electrical Conductivity and the 
Chemical Character of Solutions (Title only). May 6. 1901. Vol. xxiii. 

11. Preliminary Note on the Conductivity of Concentrated Aqueous 
Solutions of Electrolytes. November 6, 1905. Vol. xxvi. 

12. Eight papers, with others. June 22, 1908. Yol. xxviii. 

13. On an Electrically Controlled Thermostat and other Apparatus for 
the Accurate Determination of the Electrolytic Conductivity of Highly 
Conducting Solutions (with G. E. Gibson). June 22, 1908. Yol. xxx. 

14. On the Precipitation of Soluble Chlorides by Hydrochloric Acid 
(with R. B. Denison). August 20, 1910. Yol. xxx. 

In the Transactions, R.S.E. 

1. On the Relationship between Concentration and Electrolytic Con- 
ductivity in Concentrated Aqueous Solutions. May 11, 1905. Yol. xlv. 

2. The Significance of Maximum Specific Electrical Conductivity in 
Chemistry. Read July 13, 1908: published October 20, 1911. Yol. xlviii. 



VOL. xxxiv. 



19 



APPENDIX. 



CONTENTS. 



PAGE 

LAWS OF THE SOCIETY ....... 293 

THE KEITH, MAKDOUG ALL-BRISBANE, NEILL, AND GUNNING VICTORIA JUBILEE 

PRIZES ........ 298 

AWARDS OF THE KEITH, MAKDOUGALL-BRISBANE, NEILL, AND GUNNING 

VICTORIA JUBILEE PRIZES ...... 300 

PROCEEDINGS OF THE STATUTORY GENERAL MEETING, OCTOBER 1913 . 305 

PROCEEDINGS OF THE ORDINARY MEETINGS, SESSION 1913-1914 . . 306 

PROCEEDINGS OF THE STATUTORY GENERAL MEETING, OCTOBER 1914 . 312 

ACCOUNTS OF THE SOCIETY, SESSION 1913-1914 . . . 313 

THE COUNCIL OF THE SOCIETY AT OCTOBER 1914 . . . 319 

ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY AT 

JANUARY 1 , 1915 . . . . . . 320 

LIST OF HONORARY FELLOWS OF THE SOCIETY AT JANUARY 1 , 1915 . 337 

LIST OF ORDINARY FELLOWS OF THE SOCIETY ELECTED DURING SESSION 

1913-1914 ....... 339 

HONORARY FELLOWS AND ORDINARY FELLOWS DECEASED AND RESIGNED 

DURING SESSION 1913-1914 ...... 339 

LIST OF LIBRARY EXCHANGES . . . . . .340 

LIST OF PERIODICALS PURCHASED BY THE SOCIETY ... 364 

ADDITIONS TO LIBRARY DURING 1914 , BY GIFT OR PURCHASE . . 368 

INDEX . . . . . . . .370 



Laws of the Society. 



293 



LAWS OF THE SOCIETY, 

As revised October 26, 1908. 



[By the Charter of the Society (printed in the Transactions, vol. vi. p. 5), the Laws cannot he 
altered, except at a Meeting held one month after that at which the Motion for alteration 
shall have been proposed.] 



I. 

THE ROYAL SOCIETY OF EDINBURGH shall consist of Ordinary and Title. 
Honorary Fellows. 



II. 

Every Ordinary Fellow, within three months after his election, shall pay Two The fees of 
Guineas as the fee of admission, and Three Guineas as his contribution for the Fefiowsresiding 
Session in which he has been elected ; and annually at the commencement of every in Scotland - 
Session, Three Guineas into the hands of the Treasurer. This annual contribution 
shall continue for ten years after his admission, and it shall be limited to Two 
Guineas for fifteen years thereafter.* Fellows may compound for these contributions 
on such terms as the Council may from time to time fix. 



III. 

All Fellows who shall have paid Twenty-five years’ annual contribution shall be Payment to 

J cease after 

exempted from further payment. 25 years. 

IY. 

The fees of admission of an Ordinary Non-Resident Fellow shall be £26, 5s., Fees of Non- 
pay able on his admission ; and in case of any Non-Resident Fellow coming to reside ordinary 
at any time in Scotland, he shall, during each year of his residence, pay the usual rellows - 
annual contribution of £3, 3s., payable by each Resident Fellow; but after payment 
of such annual contribution for eight years, he shall be exempt from any further 
payment. In the case of any Resident Fellow ceasing to reside in Scotland, and 
wishing to continue a Fellow of the Society, it shall be in the power of the Council Resident! 
to determine on what terms, in the circumstances of each case, the privilege of 
remaining a Fellow of the Society shall be continued to such Fellow while out of 
Scotland. 

* A modification of this rule, in certain cases, was agreed to at a Meeting of the Society held on 
January 3, 1831. 

At the Meeting of the Society, on January 5, 1857, when the reduction of the Contribu- 
tions from £3, 3s. to £2, 2s., from the 11th to the 25th year of membership, was adopted, it was 
resolved that the existing Members shall share in this reduction, so far as regards their future 
annual Contributions. 



294 Proceedings of the Eoyal Society of Edinburgh. 



Defaulters. 



Privileges of 

Ordinary 

Fellows. 



Numbers 

unlimited, 



Fellows entitled 
to Transactions 
and Pro- 
ceedings. 



Mode of 
Recommending 
Ordinary 
Fellows. 



Honorary 
Fellows, British 
and Foreign. 



y. 

Members failing to pay their contributions for three successive years (due 
application having been made to them by the Treasurer) shall be reported to the 
Council, and, if they see lit, shall be declared from that period to be no longer 
Fellows, and the legal means for recovering such arrears shall be employed. 



VI. 

None but Ordinary Fellows shall bear any office in the Society, or vote in the 
choice of Fellows or Office-Bearers, or interfere in the patrimonial interests of the 
Society. 

VII-. 

The number of Ordinary Fellows shall be unlimited. 

VIII. 

All Ordinary Fellows of the Society who are not in arrear of their Annual 
Contributions shall be entitled to receive, gratis, copies of the parts of the Trans- 
actions of the Society which shall be published subsequent to their admission, upon 
application, either personally or by an authorised agent, to the Librarian, provided 
they apply for them within five years of the date of publication of such parts. 

Copies of the parts of the Proceedings shall be distributed to all Fellows of the 
Society, by post or otherwise, as soon as may be convenient after publication. 



IX. 

Candidates for admission as Ordinary Fellows shall make an application in 
writing, and shall produce along with it a certificate of recommendation to the 
purport below,* signed by at least four Ordinary Fellows, two of whom shall certify 
their recommendation from personal knowledge. This recommendation shall be 
delivered to the Secretary, and by him laid before the Council, and shall be exhibited 
publicly in the Society’s rooms for one month, after which it shall be considered by 
the Council. If the Candidate be approved by the Council, notice of the day fixed 
for the election shall be given in the circulars of at least two Ordinary Meetings of 
the Society. 



X. 

Honorary Fellows shall not be subject to any contribution. This class shall 
consist of persons eminently distinguished for science or literature. Its number 
shall not exceed Fifty-six, of whom Twenty may be British subjects, and Thirty-six 
may be subjects of foreign states. 

* “ A. B., a gentleman well versed in science (or Polite Literature, as the case may be), being 
“ to our knowledge desirous of becoming a Fellow of the Royal Society of Edinburgh, we hereby 
‘ ‘ recommend him as deserving of that honour, and as likely to prove a useful and valuable 
“Member.” 



Laws of the Society. 



295 



XI. 

Personages of Royal Blood may be elected Honorary Fellows, without regard to Royal 
the limitation of numbers' specified in Law X. 

XII. 

Honorary Fellows may be proposed by the Council, or by a recommendation (in Recommenda- 
the form given below*) subscribed by three Ordinary Fellows ; and in case the Fellows. 
Council shall decline to bring this recommendation before the Society, it shall be 
competent for the proposers to bring the same before a General Meeting. The 
election shall be by ballot, after the proposal has been communicated viva voce from Mode of 
the Chair at one Meeting, and printed in the circulars for Two Ordinary Meetings 
of the Society, previous to the day of election. 

XIII. 

The election of Ordinary Fellows shall take place only at one Afternoon Ordinary Election of 
. . d Ordinary 

Meeting of each month during the Session. The election shall be by ballot, and Fellows. 

shall be determined by a majority of at least two-thirds of the votes, provided 

Twenty-four Fellows be present and vote. 



XIY. 

The Ordinary Meetings shall be held on the first and third Mondays of each Ordinary 
month from November to March, and from May to July, inclusive ; with the Meetmgs - 
exception that when there are five Mondays in January, the Meetings for that 
month shall be held on its second and fourth Mondays. Regular Minutes shall be 
kept of the proceedings, and the Secretaries shall do the duty alternately, or accord- 
ing to such agreement as they may find it convenient to make. 



XV. 

The Society shall from time to time publish its Transactions and Proceedings. The Trans- 
For this purpose the Council shall select and arrange the papers which they shall actlons ' 
deem it expedient to publish in the Transactions of the Society, and shall super- 
intend the printing of the same. 

XVI. 

The Transactions shall be published in parts or Fasciculi at the close of each How Published. 
Session, and the expense shall be defrayed by the Society. 



* We hereby recommend — 

for the distinction of being made an Honorary Fellow of this Society, declaring that each of us 
from our own knowledge of his services to {Literature or Science , as the case may be) believe him 
to be worthy of that honour. 

(To be signed by three Ordinary Fellows. ) 



To the President and Council of the Royal Society 
of Edinburgh. 



296 Proceedings of the Royal Society of Edinburgh. 



The Council. 



Retiring 

Councillors. 



Election of 
Office-Bearers. 



Special 

Meetings ; how 
called. 



Treasurer’s 

Duties. 



Auditor. 



General 

Secretary’s 

Duties. 



XVII. 

That there shall be formed a Council, consisting — First, of such gentlemen as 
may have filled the office of President ; and Secondly, of the following to be annually 
elected, viz. : — a President, Six Vice-Presidents (two at least of whom shall be 
Resident), Twelve Ordinary Fellows as Councillors, a General Secretary, Two 
Secretaries to the Ordinary Meetings, a Treasurer, and a Curator of the Museum 
and Library. 

The Council shall have power to regulate the private business of the Society. 
At any Meeting of the Council the Chairman shall have a casting as well as a 
deliberative vote. 

XVIIL 

Four Councillors shall go out annually, to be taken according to the order in 
which they stand on the list of the Council. 



XIX. 

An Extraordinary Meeting for the election of Office-Bearers shall be held annually 
on the fourth Monday of October, or on such other lawful day in October as the 
Council may fix, and each Session of the Society shall be held to begin at the date 
of the said Extraordinary Meeting. 

XX. 

Special Meetings of the Society may be called by the Secretary, by direction of 
the Council ; or on a requisition signed by six or more Ordinary Fellows. Notice 
of not less than two days must be given of such Meetings. 

XXI. 

The Treasurer shall receive and disburse the money belonging to the Society, 
granting the necessary receipts, and collecting the money when due. 

He shall keep regular accounts of all the cash received and expended, which 
shall be made up and balanced annually ; and at the Extraordinary Meeting in 
October, he shall present the accounts for the preceding year, duly audited. At 
this Meeting, the Treasurer shall also lay before the Council a list of all arrears due 
above two years, and the Council shall thereupon give such directions as they may 
deem necessary for recovery thereof. 



XXII. 

At the Extraordinary Meeting in October, a professional accountant shall be 
chosen to audit the Treasurer’s accounts for that year, and to give the necessary 
discharge of his intromissions. 

XXIII. 

The General Secretary shall keep Minutes of the Extraordinary Meetings of the 
Society, and of the Meetings of the Council, in two distinct books. He shall, under 
the direction of the Council, conduct the correspondence of the Society, and super- 
intend its publications. For these purposes he shall, when necessary, employ a clerk, 
to be paid by the Society. 



Laws of the Society. 



297 



XXIV. 

The Secretaries to the Ordinary Meetings shall keep a regular Minute-book, in Secretaries to 
which a full account of the proceedings of these Meetings shall be entered ; they Meetings, 
shall specify all the Donations received, and furnish a list of them, and of the 
Donors’ names, to the Curator of the Library and Museum ; they shall likewise 
furnish the Treasurer with notes of all admissions of Ordinary Fellows. They shall 
assist the General Secretary in superintending the publications, and in his absence 
shall take his duty. 

XXV. 

The Curator of the Museum and Library shall have the custody and charge of curator of 
all the Books, Manuscripts, objects of Natural History, Scientific Productions, and ub?a?™ and 
other articles of a similar description belonging to the Society ; he shall take an 
account of these when received, and keep a regular catalogue of the whole, which 
shall lie in the hall, for the inspection of the Fellows. 

XXVI. 

All articles of the above description shall be open to the inspection of the Use of Museum 
Fellows at the Hall of the Society, at such times and under such regulations as the andLlbrary * 
Council from time to time shall appoint. 

XXVII. 

A Register shall be kept, in which the names of the Fellows shall be enrolled Register Book, 
at their admission, with the date. 



XXVIII. 

If, in the opinion of the Council of the Society, the conduct of any Fellow is Power of 
unbecoming the position of a Member of a learned Society, or is injurious to the Expulsion * 
character and interests of this Society, the Council may request such Fellow to 
resign ; and, if he fail to do so within one month of such request being addressed to 
him, the Council shall call a General Meeting of the Fellows of the Society to 
consider the matter ; and, if a majority of the Fellows present at such Meeting 
agree to the expulsion of such Member, he shall be then and there expelled by the 
declaration of the Chairman of the said Meeting to that effect ; and he shall there- 
after cease to be a Fellow of the Society, and his name shall be erased from the 
Roll of Fellows, and he shall forfeit all right or claim in or to the property of the 
Society. 



298 



Proceedings of the Royal Society of Edinburgh. 



THE KEITH, MAKDOUGALL-BRISBANE, NEILL, AND 
GUNNING VICTORIA JUBILEE PRIZES. 



The above Prizes will be awarded by the Council in the following manner : — 

I. KEITH PRIZE. 

The Keith Prize, consisting of a Gold Medal and from £40 to £50 in Money, 
will be awarded in the Session 1915-1916 for the “best communication on a scientific 
subject, communicated,* in the first instance, to the Royal Society during the 
Sessions 1913-1914 and 1914-1915.” Preference will be given to a paper con- 
taining a discovery. 



II. MAKDOUGALL-BRISBANE PRIZE. 

This Prize is to be awarded biennially by the Council of the Royal Society of 
Edinburgh to such person, for such purposes, for such objects, and in such manner 
as shall appear to them the most conducive to the promotion of the interests of 
science ; with the proviso that the Council shall not be compelled to award the 
Prize unless there shall be some individual engaged in scientific pursuit, or some 
paper written on a scientific subject, or some discovery in science made during the 
biennial period, of sufficient merit or importance in the opinion of the Council to 
be entitled to the Prize. 

1. The Prize, consisting of a Gold Medal and a sum of Money, will be awarded 
at the commencement of the Session 1914-1915, for an Essay or Paper having 
reference to any branch of scientific inquiry, whether Material or Mental. 

2. Competing Essays to be addressed to the Secretary of the Society, and trans- 
mitted not later than 8th July 1914. 

3. The Competition is open to all men of science. 

4. The Essays may be either anonymous or otherwise. In the former case, 
they must be distinguished by mottoes, with corresponding sealed billets, super- 
scribed with the same motto, and containing the name of the Author. 

5. The Council impose no restriction as to the length of the Essays, which may 
be, at the discretion of the Council, read at the Ordinary Meetings of the Society. 

* For the purposes of this award the word “ communicated ” shall be understood to mean the 
date on which the manuscript of a paper is received in its final form for printing, as recorded by 
the General Secretary or other responsible official. 



299 



Keith, Brisbane, Neill, and Gunning Prizes. 

They wish also to leave the property and free disposal of the manuscripts to the 
Authors ; a copy, however, being deposited in the Archives of the Society, unless 
the paper shall be published in the Transactions. 

6. In awarding the Prize, the Council will also take into consideration any 
scientific papers presented* to the Society during the Sessions 1912-13, 1913-14, 
whether they may have been given in with a view to the prize or not. 



III. NEILL PRIZE. 

The Council of the Royal Society of Edinburgh having received the bequest of 
the late Dr Patrick Neill of the sum of £500, for the purpose of “the interest 
thereof being applied in furnishing a Medal or other reward every second or third 
year to any distinguished Scottish Naturalist, according as such Medal or reward 
shall be voted by the Council of the said Society,” hereby intimate : 

1. The Neill Prize, consisting of a Gold Medal and a sum of Money, will be 
awarded during the Session 1915-1916. 

2. The Prize will be given for a Paper of distinguished merit, on a subject of 
Natural History, by a Scottish Naturalist, which shall have been presented* to the 
Society during the two years preceding the fourth Monday in October 1915, — or 
failing presentation of a paper sufficiently meritorious, it will be awarded for a work 
or publication by some distinguished Scottish Naturalist, on some branch of Natural 
History, bearing date within five years of the time of award. 



IV. GUNNING VICTORIA JUBILEE PRIZE. 

This Prize, founded in the year 1887 by Dr R. H. Gunning, is to be awarded 
quadrennially by the Council of the Royal Society of Edinburgh, in recognition of 
original work in Physics, Chemistry, or Pare or Applied Mathematics. 

Evidence of such work may be afforded either by a Paper presented to the 
Society, or by a Paper on one of the above subjects, or some discovery in them 
elsewhere communicated or made, which the Council may consider to be deserving 
of the Prize. 

The Prize consists of a sum of money, and is open to men of science resident in 
or connected with Scotland. The first award was made in the year 1887. 

In accordance with the wish of the Donor, the Council of the Society may on 
fit occasions award the Prize for work of a definite kind to be undertaken during 
the three succeeding years by a scientific man of recognised ability. 

* For the purposes of this award the word ‘ ‘ presented ” shall be understood to mean the date 
on which the manuscript of a paper is received in its final form for printing, as recorded by the 
General Secretary or other responsible official. 



300 Proceedings of the Royal Society of Edinburgh. 



AWARDS OF THE KEITH, MAKDOUGALL - BRISBANE, 
NEILL, AND GUNNING VICTORIA JUBILEE PRIZES. 

I. KEITH PRIZE. 

1st Biennial Period, 1827-29.— Dr Brewster, for his papers “on his Discovery of Two New 
Immiscible Fluids in the Cavities of certain Minerals,” published in the Transactions of 
the Society. 

2nd Biennial Period, 1829-31. — Dr Brewster, for his paper “on a New Analysis of Solar 
Light,” published in the Transactions of the Society. 

3rd Biennial Period, 1831-33. — Thomas Graham, Esq., for his paper “on the Law of the 
Diffusion of Gases,” published in the Transactions of the Society. 

4th Biennial Period, 1833-35. — Professor J. D. Forbes, for his paper “on the Refraction and 
Polarization of Heat,” published in the Transactions of the Society. 

5th Biennial Period, 1835-37. — John Scott Russell, Esq., for his researches “on Hydro- 
dynamics,” published in the Transactions of the Society. 

6th Biennial Period, 1837-39. — Mr John Shaw, for his experiments “on the Development 
and Growth of the Salmon,” published in the Transactions of the Society. 

7th Biennial Period, 1839-41. — Not awarded. 

8th Biennial Period, 1841-1843. — Professor James David Forbes, for his papers “on 
Glaciers,” published in the Proceedings of the Society. 

9th Biennial Period, 1843-45. — Not awarded. 

10th Biennial Period, 1845-47. — General Sir Thomas Brisbane, Bart., for the Makerstoun 
Observations on Magnetic Phenomena, made at his expense, and published in the Trans- 
actions of the Society. 

11th Biennial Period, 1847-49. — Not awarded. 

12th Biennial Period, 1849-51. — Professor Kelland, for his papers “on General Differentia- 
tion, including his more recent Communication on a process of the Differential Calculus, and 
its application to the solution of certain Differential Equations,” published in the Transac- 
tions of the Society. 

13th Biennial Period, 1851-53. — W. J. Macquorn Rankine, Esq., for his series of papers 
“on the Mechanical Action of Heat,” published in the Transactions of the Society. 

14th Biennial Period, 1853-55. — Dr Thomas Anderson, for his papers “on the Crystalline 
Constituents of Opium, and on the Products of the Destructive Distillation of Animal 
Substances,” published in the Transactions of the Society. 

15th Biennial Period, 1855-57. — Professor Boole, for his Memoir “on the Application of 
the Theory of Probabilities to Questions of the Combination of Testimonies and Judgments,” 
published in the Transactions of the Society. 

16th Biennial Period, 1857-59. — Not awarded. 

17th Biennial Period, 1859-61. — John Allan Broun, Esq., F.R.S., Director of the Trevandrum 
Observatory, for his papers “on the Horizontal Force of the Earth’s Magnetism, on the 
Correction of the Bifilar Magnetometer, and on Terrestrial Magnetism generally,” published 
in the Transactions of the Society. 

18th Biennial Period, 1861-63. — Professor William Thomson, of the University of Glasgow, 
for his Communication ‘ ‘ on some Kinematical and Dynamical Theorems. ” 

19th Biennial Period, 1863-65. — Principal Forbes, St Andrews, for his “Experimental 
Inquiry into the Laws of Conduction of Heat in Iron Bars,” published in the Transactions 
of the Society. 

20th Biennial Period, 1865-67. — Professor C. Piazzi Smyth, for his paper “on Recent 
Measures at the Great Pyramid,” published in the Transactions of the Society. 

21st Biennial Period, 1867-69. — Professor P. G. Tait, for his paper “on the Rotation of a 
Rigid Body about a Fixed Point,” published in the Transactions of the Society. 

22nd Biennial Period, 1869-71. — Professor Clerk Maxwell, for his paper “on Figures, 
Frames, and Diagrams of Forces,” published in the Transactions of the Society. 



301 



Keith, Brisbane, Neill, and Gunning Prizes. 

23rd Biennial Period, 1871-73. — Professor P. G. Tait, for his paper entitled “First Approxi- 
mation to a Thermo-electric Diagram,” published in the Transactions of the Society. 

24th Biennial Period, 1873-75. — Professor Crum Brown, for his Researches “on the Sense of 
Rotation, and on the Anatomical Relations of the Semicircular Canals of the Internal Ear.” 

25th Biennial Period, 1875-77.— Professor M. Forster Heddle, for his papers “on the 
Rhombohedral Carbonates, ” and “on the Felspars of Scotland,” published in the Transac- 
tions of the Society. 

26th Biennial Period, 1877-79. — Professor H. C. Fleeming Jenkin, for his paper “on the 
Application of Graphic Methods to the Determination of the Efficiency of Machinery,” 
published in the Transactions of the Society ; Part II. having appeared in the volume for 
1877-78. 

27th Biennial Period, 1879-81. — Professor George Chrystal, for his paper “on the Differ- 
ential Telephone,” published in the Transactions of the Society. 

28th Biennial Period, 1881-83. — Thomas Muir, Esq., LL.D., for his “Researches into the 
Theory of Determinants and Continued Fractions,” published in the Proceedings of the Society. 

29th Biennial Period, 1883-85. — John Aitken, Esq., for his paper “on the Formation of 
Small Clear Spaces in Dusty Air,” and for previous papers on Atmospheric Phenomena, 
published in the Transactions of the Society. 

30th Biennial Period, 1885-87. — John Young Buchanan, Esq., for a series of communica- 
tions, extending over several years, on subjects connected with Ocean Circulation, 
Compressibility of Glass, etc. ; two of which, viz., “On Ice and Brines,” and “On the 
Distribution of Temperature in the Antarctic Ocean,” have been published in the Proceedings 
of the Society. 

31st Biennial Period, 1887-89. — Professor E. A. Letts, for his papers on the Organic 
Compounds of Phosphorus, published in the Transactions of the Society. 

32nd Biennial Period, 1889-91. — R. T. Omond, Esq., for his contributions to Meteorological 
Science, many of which are contained in vol. xxxiv. of the Society’s Transactions. 

33rd Biennial Period, 1891-93. — Professor Thomas R. Fraser, F.R.S., for his papers on 
Strophanthus hispidus, Strophanthin, and Strophanthidin, read to the Society in February 
and June 1889 and in December 1891, and printed in vols. xxxv. , xxxvi., and xxxvii. 
of the Society’s Transactions. 

34th Biennial Period, 1893-95. — Dr Cargill G. Knott, for his papers on the Strains produced 
by Magnetism in Iron and in Nickel, which have appeared in the Transactions and 
Proceedings of the Society. 

35th Biennial Period, 1895-97. — Dr Thomas Muir, for his continued communications on 
Determinants and Allied Questions. 

36th Biennial Period, 1897-99. — Dr James Burgess, for his paper “on the Definite Integral 

— — / e ~ p dt, with extended Tables of Values,” printed in vol. xxxix. of the Transactions 
o 

of the Society. 

37th Biennial Period, 1899-1901. — Dr Hugh Marshall, for his discovery of the Persulphates, 
and for his Communications on the Properties and Reactions of these Salts, published in the 
Proceedings of the Society. 

38th Biennial Period, 1901-03.— Sir William Turner, K.C.B., LL.D., F.R.S., &c., for his 
memoirs entitled “ A Contribution to the Craniology of the People of Scotland,” published in 
the Transactions of the Society, and for his “ Contributions to the Craniology of the People 
of the Empire of India,” Parts I., II., likewise published in the Transactions of the Society. 

39th Biennial Period, 1903-05. — Thomas H. Bryce, M.A., M.D., for his two papers on “The 
Histology of the Blood of the Larva of Lepidosiren paradoxa , ” published in the Transactions 
of the Society within the period. 

40th Biennial Period, 1905-07.— Alexander Bruce, M.A., M.D., F.R.C.P.E., for his paper 
entitled “ Distribution of the Cells in the Intermedio-Lateral Tract of the Spinal Cord,” 
published in the Transactions of the Society within the period. 

41st Biennial Period, 1907-09. — Wheelton Hind, M.D., B.S., F.R.C.S., F.G.S., for a paper 
published in the Transactions of the Society, ‘ ‘ On the Lamellibranch and Gasteropod Fauna 
found in the Millstone Grit of Scotland.” 

42nd Biennial Period, 1909-11. — Professor Alexander Smith, B.Sc., Ph.D., of New York, 
for his researches upon “Sulphur” and upon “Vapour Pressure,” appearing in the 
Proceedings of the Society. 

43rd Biennial Period, 1911-1913. — James Russell, Esq., for his series of investigations 
relating to magnetic phenomena in metals and the molecular theory of magnetism, the 
results of which have been published in the Proceedings and Transactions of the Society, 
the last paper having been issued within the period. 



302 



Proceedings of the Royal Society of Edinburgh. 



II. MAKDOUG ALL-BRISBANE PKIZE. 

1st Biennial Period, 1859. — Sir Roderick Impey Murchison, on account of his Contributions 
to the Geology of Scotland. 

2nd Biennial Period, 1860-62.— William Seller, M.D., F.R.C.P.E., for his “ Memoir of the 
Life and Writings of Dr Robert Whytt,” published in the Transactions of the Society. 

3rd Biennial Period, 1862-64.— John Denis Macdonald, Esq., R.N., F.R.S., Surgeon of 
H.M.S. “ Icarus,” for his paper “on the Representative Relationships of the Fixed and Free 
Tunicata, regarded as Two Sub-classes of equivalent value ; with some General Remarks on 
their Morphology,” published in the Transactions of the Society. 

4th Biennial Period, 1864-66. — Not awarded. 

5th Biennial Period, 1866-68. — Dr Alexander Crum Brown and Dr Thomas Richard 
Fraser, for their conjoint paper “on the Connection between Chemical Constitution and 
Physiological Action,” published in the Transactions of the Society. 

6th Biennial Period, 1868-70. — Not awarded. 

7th Biennial Period, 1870-72.— George James Allman, M.D., F.R.S., Emeritus Professor of 
Natural History, for his paper “on the Homological Relations of the Coelenterata,” published 
in the Transactions, which forms a leading chapter of his Monograph of Gymnoblastic or 
Tubularian Hydroids — since published. 

8th Biennial Period, 1872-74. — Professor Lister, for his paper “on the Germ Theory of 
Putrefaction and the Fermentive Changes,” communicated to the Society, 7th April 1873. 

9th Biennial Period, 1874-76. — Alexander Buchan, A.M., for his paper “ on the Diurnal 
Oscillation of the Barometer,” published in the Transactions of the Society. 

10th Biennial Period, 1876-78. — Professor Archibald Geikie, for his paper “on the Old 
Red Sandstone of Western Europe,” published in the Transactions of the Society. 

11th Biennial Period, 1878-80. — Professor Piazzi Smyth, Astronomer-Royal for Scotland, for 
his paper “on the Solar Spectrum in 1877-78, with some Practical Idea of its probable 
Temperature of Origination,” published in the Transactions of the Society. 

12th Biennial Period, 1880-82. — Professor James Geikie, for his “Contributions to the 
Geology of the North-West of Europe,” including his paper “on the Geology of the 
Faroes,” published in the Transactions of the Society. 

13th Biennial Period, 1882-84. — Edward Sang, Esq., LL.D., for his paper “on the Need of 
Decimal Subdivisions in Astronomy and Navigation, and on Tables requisite therefor,” and 
generally for his Recalculation of Logarithms both of Numbers and Trigonometrical Ratios, 
— the former communication being published in the Proceedings of the Society. 

14th Biennial Period, 1884-86. — John Murray, Esq., LL.D., for his papers “On the Drainage 
Areas of Continents, and Ocean Deposits,” “ The Rainfall of the Globe, and Discharge of 
Rivers,” “ The Height of the Land and Depth of the Ocean,” and “The Distribution of 
Temperature in the Scottish Lochs as affected by the Wind.” 

15th Biennial Period, 1886-88. — Archibald Geikie, Esq., LL.D., for numerous Communica- 
tions, especially that entitled “ History of Volcanic Action during the Tertiary Period in the 
British Isles,” published in the Transactions of the Society. 

16th Biennial Period, 1889-90. — Dr Ludwig Becker, for his paper on “ The Solar Spectrum at 
Medium and Low Altitudes, ” printed in vol. xxx vi. Part I. of the Society’s Transactions. 

1 7th Biennial Period, 1890-92. — Hugh Robert Mill, Esq., D.Sc., for his papers on “The 
Physical Conditions of the Clyde Sea Area,” Part I. being already published in vol. xxxvi. 
of the Society’s Transactions. 

18th Biennial Period, 1892-94. — Professor James Walker, D.Sc., Ph.D., for his work on 
Physical Chemistry, part of which has been published in the Proceedings of the Society, vol. 
xx. pp. 255-263. In making this award, the Council took into consideration the work 
done by Professor Walker along with Professor Crum Brown on the Electrolytic Synthesis of 
Dibasic Acids, published in the Transactions of the Society. 

19th Biennial Period, 1894-96. — Professor John G. M‘Kendrick, for numerous Physiological 
papers, especially in connection with Sound, many of which have appeared in the Society’s 
publications. 

20th Biennial Period, 1896-98.— Dr William Peddie, for his papers on the Torsional Rigidity 
of Wires. 

21st Biennial Period, 1898-1900. — Dr Ramsay H. Traquair, for his paper entitled “ Report on 
Fossil Fishes collected by the Geological Survey in the Upper Silurian Rocks of Scotland,” 
printed in vol. xxxix. of the Transactions of the Society. 



Keith, Brisbane, Neill, and Gunning Prizes. 303 

22nd Biennial Period, 1900-02. — Dr Arthur T. Masterman, for his paper entitled “The 
Early Development of Cribrella oculata (Forbes), with remarks on Echinoderm Development,” 
printed in vol. xl. of the Transactions of the Society. 

23rd Biennial Period, 1902-04. — Mr John Dougall, M.A., for his paper on “An Analytical 
Theory of the Equilibrium of an Isotropic Elastic Plate,” published in vol. xli. of the 
Transactions of the Society. 

24th Biennial Period, 1904-06.— Jacob E. Halm, Ph.D., for his two papers entitled “Spectro- 
scopic Observations of the Rotation of the Sun,” and “ Some Further Results obtained with 
the Spectroheliometer,” and for other astronomical and mathematical papers published in 
the Transactions and Proceedings of the Society within the period. 

25th Biennial Period, 1906-08. — D. T. Gw ynne- Vaughan, M.A., F.L.S., for his papers, 
1st, “On the Fossil Osmundacese,” and 2nd, “ On the Origin of the Adaxially-curved Leaf- 
trace in the Filicales,” communicated by him conjointly with Dr R. Kidston. 

26th Biennial Period, 1908-10. — Ernest MacLagan Wedderburn, M.A., LL.B., for his 
series of papers bearing upon “The Temperature Distribution in Fresh-water Lochs,” and 
especially upon “The Temperature Seiche.” 

27th Biennial Period, 1910-12.— John Brownlee, M.A., M.D., D.Sc., for his contributions 
to the Theory of Mendelian Distributions and cognate subjects, published in the Proceedings 
of the Society within and prior to the prescribed period. 



III. THE NEILL PRIZE. 

1st Triennial Period, 1856-59. — Dr W. Lauder Lindsay, for his paper “ on the Spermogones 
and Pycnides of Filamentous, Fruticulose, and Foliaceous Lichens,” published in the Trans- 
actions of the Society. 

2nd Triennial Period, 1859-61. — Robert Kaye Greville, LL.D., for his Contributions to 
Scottish Natural History, more especially in the department of Cryptogamic Botany, 
including his recent papers on Diatomacese. 

3rd Triennial Period, 1862-65. — Andrew Crombie Ramsay, F.R.S., Professor of Geology in 
the Government School of Mines, and Local Director of the Geological Survey of Great 
Britain, for his various works and memoirs published during the last five years, in which he 
has applied the large experience acquired by him in the Direction of the arduous work of 
the Geological Survey of Great Britain to the elucidation of important questions bearing on 
Geological Science. 

4th Triennial Period, 1865-68. — Dr William Carmichael MHntosh, for his paper “on the 
Structure of the British Nemerteans, and on some New British Annelids,” published in the 
Transactions of the Society. 

5th Triennial Period, 1868-71. — Professor William Turner, for his papers “on the Great 
Finner Whale ; and on the Gravid Uterus, and the Arrangement of the Foetal Membranes 
in the Cetacea, ” published in the Transactions of the Society. 

6th Triennial Period, 1871-74. — Charles William Peach, Esq., for his Contributions to 
Scottish Zoology and Geology, and for his recent contributions to Fossil Botany. 

7th Triennial Period, 1874-77. — Dr Ramsay H. Traquair, for his paper “on the Structure 
and Affinities of Tristichopterus alatus (Egerton),” published in the Transactions of the 
Society, and also for his contributions to the Knowledge of the Structure of Recent and 
Fossil Fishes. 

8th Triennial Period, 1877-80. — John Murray, Esq., for his paper “ on the Structure and 
Origin of Coral Reefs and Islands,” published (in abstract) in the Proceedings of the Society. 

9th Triennial Period, 1880-83. — Professor Herdman, for his papers “on the Tunicata,” 
published in the Proceedings and Transactions of the Society. 

10th Triennial Period, 1883-86.— B. N. Peach, Esq., for his Contributions to the Geology and 
Palseontology of Scotland, published in the Transactions of the Society. 

11th Triennial Period, 1886-89. — Robert Kidston, Esq., for his Researches in Fossil Botany, 
published in the Transactions of the Society. 

12th Triennial Period, 1889-92. — John Horne, Esq., F.G.S., for his Investigations into the 
Geological Structure and Petrology of the North-West Highlands. 

13th Triennial Period, 1892-95. — Robert Irvine, Esq., for his papers on the Action of 
Organisms in the Secretion of Carbonate of Lime and Silica, and on the solution of these 
substances in Organic Juices. These are printed in the Society’s Transactions and 
Proceedings. 



304 



Proceedings of the Royal Society of Edinburgh. 

14th Triennial Period, 1895-98. — Professor Cossar Ewart, for his recent Investigations con- 
nected with Telegony. 

15th Triennial Period, 1898-1901. — Dr John S. Flett, for his papers entitled “The Old Red 
Sandstone of the Orkneys ” and ‘ ‘ The Trap Dykes of the Orkneys, ’* printed in vol. 
xxxix. of the Transactions of the Society. 

16th Triennial Period, 1901-04. — Professor J. Graham Kerr, M.A., for his Researches on 
Lepidosiren paradoxa, published in the Philosophical Transactions of the Royal Society, 
London. 

17th Triennial Period, 1904-07. — Frank J. Cole, B.Sc., for his paper entitled “ A Monograph 
on the General Morphology of the Myxinoid Fishes, based on a study of Myxine,” published 
in the Transactions of the Society, regard being also paid to Mr Cole’s other valuable contri- 
butions to the Anatomy and Morphology of Fishes. 

1st Biennial Period, 1907-09. — Francis J. Lewis, M.Sc. , F.L.S., for his papers in the Society’s 
Transactions “ On the Plant Remains of the Scottish Peat Mosses.” 

2nd Biennial Period, 1909-11. — James Murray, Esq., for his paper on “Scottish Rotifers 
collected by the Lake Survey (Supplement),” and other papers on the “Rotifera” and 
“ Tardigrada, ” which appeared in the Transactions of the Society — (this Prize was awarded 
after consideration of the papers received within the five years prior to the time of award : 
see Neill Prize Regulations). 

3rd Biennial Period, 1911-13. — Dr W. S. Bruce, in recognition of the scientific results of his 
Arctic and Antarctic explorations. 



IV. GUNNING VICTORIA JUBILEE PRIZE. 

1st Triennial Period, 1884-87. — Sir William Thomson, Pres. R.S.E., F.R.S., for a remark- 
able series of papers “on Hydrokinetics,” especially on Waves and Vortices, which have 
been communicated to the Society. 

2nd Triennial Period, 1887-90. — Professor P. G. Tait, Sec. R.S.E., for his work in connection 
with the “ Challenger” Expedition, and his other Researches in Physical Science. 

3rd Triennial Period, 1890-93. — Alexander Buchan, Esq., LL.D., for his varied, extensive, 
and extremely important Contributions to Meteorology, many of which have appeared in the 
Society’s Publications. 

4th Triennial Period, 1893-96. — John Aitken, Esq., for his brilliant Investigations in 
Physics, especially in connection with the Formation and Condensation of Aqueous Vapour. 

1st Quadrennial Period, 1896-1900. — Dr T. D. Anderson, for his discoveries of New and 
Variable Stars. 

2nd Quadrennial Period, 1900-04. — Sir James Dewar, LL.D., D.C.L., F.R.S., etc., for his 
researches on the Liquefaction of Gases, extending over the last quarter of a century, and 
on the Chemical and Physical Properties of Substances at Low Temperatures : his earliest 
papers being published in the Transactions and Proceedings of the Society. 

3rd Quadrennial Period, 1904-08. — Professor George Chrystal, M.A. , LL.D., for a series of 
papers on “ Seiches,” including “The Hydrodynamical Theory and Experimental Investiga- 
tions of the Seiche Phenomena of Certain Scottish Lakes. ” 

4th Quadrennial Period, 1908-12. — Professor J. Norman Collie, Ph.D., F.R.S., for his 
distinguished contributions to Chemistry, Organic and Inorganic, during twenty-seven 
years, including his work upon Neon and other rare gases. Professor Collie’s early papers 
were contributed to the Transactions of the Society. 



Meetings of the Society. 



305 



PROCEEDINGS OF THE STATUTORY GENERAL MEETING 
Beginning the 131st Session, 1913-1914. 



At the Annual Statutory Meeting of the Royal Society of Edinburgh, held in the Society’s 
Lecture Room, 24 George Street, on Monday, October 27, 1913, at 4.30 p.m. 

Principal Sir, Wm. Turner, K.C.B. , President, in the Chair. 

Before the ordinary business of the Meeting commenced, Professor Crum Brown, in the name 
of Lady Kelvin, presented to the Society a Marble Bust of the late Lord Kelvin, and the 
President, Sir Wm. Turner, received the Bust in the name of the Society. (For account of the 
Ceremony of the Presentation and Reception, see Proceedings, vol. xxxiv, pp. 1-3.) 

The Minutes of the last Statutory Meeting, October 28, 1912, were read, approved, and signed. 

On the motion of Dr Horne, seconded by Mr Jas. Currie, Mr John Alison and Mr J. B. 
Clark were appointed Scrutineers, and the ballot for the New Council commenced. 

The Treasurer’s Accounts for the past year, 1912-1913, were submitted; these, with the 
Auditors’ Report, were read, and approved. 



The Scrutineers reported that the following Council had been duly elected : — 



Professor James Geikie, LL.D., D.C.L., F.R.S., F.G.S., President 
James Burgess, C.I.E., LL.D., M.R.A.S., 

Professor T. Hudson Beare, M.Inst.C.E., 

Professor F. 0. Bower, M.A., D.Sc., F.R.S., 

Professor Sir Thomas R. Fraser, M.D., LL.D., ^ Vice-Presidents. 



F. R.C.P.E., F.R.S., 

Benjamin N. Peach, LL.D., F.R.S., F.G.S., 

Professor Sir E. A. Schafer, M.R.C.S., LL.D., F.R.S.,, 

Cargill G. Knott, D.Sc., General Secretary. 

Robert Kidston, LL.D., F.R.S., F.G.S., \ Secretaries to Ordinary 

Professor Arthur Robinson, M.D., M.R.C.S., J Meetings. 

James Currie, M.A. , Treasurer. 

John S. Black, M.A. , LL.D., Curator of Library and Museum. 



ORDINARY MEMBERS OF COUNCIL. 



Professor T. H. Bryce, M.A., M.D. 

William Allan Carter, M.Inst.C.E. 
Andrew Watt, M.A. 

James H. Ashworth, D.Sc. 

James Gordon Gray, D.Sc. 

Professor R. A. Sampson, M.A., D.Sc., F.R.S. 
Professor D’Arcy W. Thompson, C.B., B.A., 
F.L.S. 



Professor E. T. Whittaker, Sc.D., F.R.S. 
Principal A. P. Laurie, M.A., D.Sc. 

Professor J. Graham Kerr, M.A., F.R.S. 
Leonard Dobbin, Ph.D. 

Ernest Maclagan Wedderburn, M.A., 
LL.B. 



^° C George^Heriot’s^rast) n } William A llan Ca ETER , M.Inst.C.E. 

On the motion of Professor F. 0. Bower, thanks were voted to the Scrutineers. 

On the motion of Mr Hewat, thanks were voted to the Auditors, Messrs Lindsay, Jamieson 
& Haldane, and they were reappointed. 

On the motion of Dr Knott, thanks were voted to the Treasurer, Mr James Currie. 



YOL. XXXIV. 



20 



306 



Proceedings of the Royal Society of Edinburgh. [Sess. 



PROCEEDINGS OF THE ORDINARY MEETINGS, 
Session 1913-1914. 



FIRST ORDINARY MEETING. 



Monday , November 3, 1913. 

Professor James Geikie, LL.D., D.C.L , F.R.S., F.G.S., President, in the Chair. 

The President opened the Session with a short Address. 

The following Communications were read : — 

1. Atmospheric Electric Potential Results at Edinburgh during 1912. By G. A. Cause, 
M.A. , D.Sc., and G. Shearer, M.A., B.Sc. ( With Lantern Illustrations.) 

2. Some Factorable Minors of a Compound Determinant. By Professor W. H. Metzler, 
A.B., Ph. D. 

3. An Analytical Theory of the Equilibrium of an Isotropic Elastic Rod of Circular Section. 
By Dr John Dougall. Communicated by Professor G. A. Gibson, LL.D. 



The following, nominated for Honorary Fellowship, were balloted for, and duly declared 
elected : — 



As British Honorary Fellows : — 



1. Horace Lamb, M.A., Sc.D. , D.Sc., LL.D., F.R.S., Professor of Mathematics in the 
University of Manchester. 

2. Sir William Turner Thiselton-Dyer, K.C.M.G., C.I.E., M.A., LL.D., F.R.S., formerly 
Director of the Royal Botanic Gardens, Kew. 



As Foreign Honorary Fellows : — 

1. George Ellery Hale, F.M.R.S., Director of the Mount Wilson Solar Observatory 
(Carnegie Institute of Washington). 

2. Emil Clement Jungfleisch, Mem. Inst. Fr., Professor of Organic Chemistry in the 
College of France, Paris. 

3. Santiago Ramon y Cajal, F.M.R.S., Professor of Histology and Pathological Anatomy in 
the University of Madrid. 

4. Vito Yolterra, F.M.R.S., Sc.D., Ph.D., Professor of Mathematics and Physics in the 
University of Rome. 

5. Charles Ren& Zeiller, Mem. Inst. Fr. , Professor of Plant Palajontology in the National 
Superior School of Mines, Paris. 



SECOND ORDINARY MEETING. 

Monday , November 17, 1913. 

Professor James Geikie, LL.D., D.C.L., F.R.S., F.G.S., President, in the Chair. 

The following Communications were read : — 

1. On the Fossil Flora of the Staffordshire Coal Fields. Part III. — The Fossil Flora of the 
Westphalian Series of the South Staffordshire Coalfield. By Dr R. Kidston, F.R.S. ( With 
Lantern Illustrations. ) 

2. Sphcerostoma ovale ( Conostoma ovale et intermedium , Williamson), a Lower Carboniferous 
Ovale from Pettycur, Fifeshire, Scotland. By Professor Margaret J. Benson, D.Sc. Com- 
municated by Dr R. Kidston, F.R.S. 

3. Studies on the Pharmacological Action of Tetra-alkyl-ammonium Compounds. I. — The 
Action of Tetra-methyl-ammonium Chloride. By Professor C. R. Marshall, M.D. ( With 
Lantern Illustrations.) 

4. The Theory of Bigradients from 1859-1880. By Dr Thomas Muir, F.R.S. 

The following Candidate for Fellowship was balloted for, and duly declared elected : — 
Edward Philtp Harrison, Ph.D. 



1913-14.] 



Meetings of the Society. 



307 



THIRD ORDINARY MEETING. 

Monday , December 1, 1913. 

Professor J. Hudson Beare, B.Sc., M. Inst.C.E., "Vice-President, in the Chair. 

At the request of the Council the following Address was delivered : — 

Principia Atmospherica : A Study of the Circulation of the Atmosphere. By W. N. Shaw, 
LL.D., Sc.D., F.R.S. , Director of the Meteorological Office, London. ( With Lantern 
Illustrations . ) 

The following Communications were also read : — 

1. Observations on the Auditory Organ in the Cetacea. By Principal Sir William Turner, 
K.C.B. 

2. Note on a Siliceous Sponge of the Order Hexactinellida from South Shetland. By Principal 
Sir William Turner, K.C.B. 

The following Candidates for Fellowship were balloted for, and declared duly elected : — John 
William Pare, M.B., C.M. (Edin.), M.D., L.D.S. (Eng.), William Fraser, William Barron 
Coutts, M.A., B.S., Alfred Oswald, and John Edward Gemmell, M.B., C.M. (Edin.). 



FOURTH ORDINARY MEETING. 

Monday , December 15, 1913, 

Professor James Geikie, LL.D., D.C.L. , F.R.S. , F.G.S. , President, in the Chair. 

The following Communications were read : — 

1. Obituary Notice of Dr R. M. Ferguson. By Dr A. E. Scougal, M.A. 

2. Studies on the Pharmacological Action of Tetra-alkyl-ammonium Compounds. II. — The 

Action of Tetra - ethyl - ammonium Chloride. III. — The Action of Methyl - ethyl - ammonium 

Chlorides. By Professor C. R. Marshall, M.D. ( With Lantern Illustrations.) 

3. Enzymatic Peptolysis in Germinating Seeds. — Parts I. and II. By Miss Dorothy Court, 
B.Sc. Communicated by Professor E. Westergaard, Ph. D. 

4. The Kinetic Energy of Viscous Flow through a Circular Tube. By Professor A. H. Gibson, 
D.Sc. 

5. Polychseta of the Family Nereidse collected by the Scottish National Antarctic Expedition. 
By L. N. G. Ramsay, M.A., B.Sc. Communicated by Dr J. H. Ashworth. 



FIFTH ORDINARY MEETING. 

Monday , January 19, 1914. 

Professor James Geikie, LL.D., D.C.L., F.R.S., F.G.S. , President, in the Chair. 

The following Communications were read : — 

1. The Place in Nature of the Tasmanian Aboriginal as deduced from a Study of his Calvaria. 
Part II. — His Relation to the Australian Aboriginal. By Professor R. J. A. Berry and Dr 
A. W. D. Robertson. 

2. A Study of the Curvatures of the Tasmanian Aboriginal Cranium. By Mr L. W. G. Buchner. 
Communicated by Professor R. J. A. Berry. (In the absence of Professor Berry a brief account 
of the above two papers was given by Dr Gerald Leighton.) 

3. The Path of a Ray of Light in a Rotating Homogeneous and Isotropic Solid. By E. M. 
Anderson, M.A., B.Sc. Communicated by the General Secretary. 

4. The Anatomy of a New Species of Bathydoris and the Affinities of the Genus: Scottish 
National Antarctic Expedition. By T. J. Evans, M.A. Communicated by Dr J. H. Ashworth. 
( With Lantern Illustrations. ) 

5. On the Genus Porponia and related Genera : Scottish National Antarctic Expedition. By 
Professor Oskar Carlgren. Communicated by Dr W. S. Bruce. {With Lantern Illustrations.) 

The following Candidates for Fellowship were balloted for, and declared duly elected : — 
Joseph Pearson, D.Sc., F.L.S., Director of the Colombo Museum, and Marine Biologist to the 
Ceylon Government, Colombo Museum, Ceylon; Spencer Mort, M.B., Ch. B., Medical Super- 



308 



Proceedings of the Royal Society of Edinburgh. [Sess. 



intendent, Edmonton Infirmary, London, N. ; and Charles Gloyer Barkla, D.Sc., F.R.S., 
Professor of Natural Philosophy in the University of Edinburgh, Littledene, 34 Priestfield 
Road, Edinburgh. 

Mr W. B. Coutts, D.Sc., M.A., signed the Roll, and was duly admitted a Fellow of the 
Society. 



SIXTH ORDINARY MEETING. 

Monday , February 2, 1914. 

Professor James Geikie, LL.D., D.C.L., F.R.S., F.G.S., President, in the Chair. 

At the request of the Council the following Address was delivered : — 

Notes on the Evolution of Antarctica. By T. W. Edgeworth David, C.M.G., Hon. D.Sc. 
Oxon., F.R.S., Professor of Geology in the University of Sydney, N.S.W. ; Scientific Officer with 
the Shackleton Expedition, 1907-09 ; Leader of Party which reached South Magnetic Pole. ( With 
Lantern Illustrations . ) 



SEVENTH ORDINARY MEETING. 

Monday , February 16, 1914. 

Professor James Geikie, LL.D., D.C.L. , F.R.S. , F.G. S., President, in the Chair. 

The following Communications were read : — 

1. The Axial Inclination of Curves of Thermoelectric Force : A Case from the Thermoelectrics 
of Strained Wires. By John M‘Whan, M.A., Ph.D. Communicated by Professor Andrew 
Gray, LL.D., F.R.S. 

2. Rupture Strains in Beams and Crane Hooks. By Angus R. Fulton, B.Sc., A. M. Inst.C.E. 
Communicated by Professor A. H. Gibson, D.Sc. 

3. A Description of the Systematic Anatomy of a Foetal Sea-Leopard ( Stenorhynchus leptonyx), 
with Remarks upon the Microscopic Anatomy of some of the Organs. By Harold A. Haig, 
M. B., B.S., M.R.C.S. Communicated by Professor Arthur Robinson, M.D., M.R.C.S. ( With 
Lantern Illustrations. ) 

The following Candidates for Fellowship were balloted for, and declared duly elected : — Robert 
John Harvey-Gibson, M.A., F.L.S., Professor of Botany, University of Liverpool, 22 Falkner 
Square, Liverpool, and John Noble Jack, Professor of Agriculture to the County Council of 
Sussex, Kingscote, The Avenue, Lewes, Sussex. 



EIGHTH ORDINARY MEETING. 

Monday, March 2, 1914. 

Professor Sir E. A. Schafer, F.R.S., Vice-President, in the Chair. 

The following Communications were read : — 

1. The Electrolytic Treatment of Lead Poisoning. By Professor Sir Thomas Oliver, M.D., 
LL.D., F.R.C.P., and Mr T. M. Clague. ( With a Demonstration and with Lantern 
Illustrations. ) 

2, The Aborigines of Tasmania. Part III. — The Hair of the Head, compared with that of 
other Ulotrichi, and with Australians and Polynesians. By Principal Sir William Turner, K.C.B. 



NINTH ORDINARY MEETING. 

Monday, March 16, 1914. 

Professor James Geikie, LL.D., D.C.L., F.R.S., F.G.S., President, in the Chair. 

The following Communications were read : — 

1. Stalk-eyed Crustacea Malacostraca of the Scottish National Antarctic Expedition. By the 
Rev. T. R. R. Stebbing, M.A., F.R.S. Communicated by Dr J. H. Ashworth. 



309 



1913-L4.] Meetings of the Society. 

2. Note on the Atmospheric Electrical Potential Gradient in Industrial Districts. By Mr 
Daniel W. Steuart and Mr Ingvar Jorgensen. Communicated by James A. S. 
Watson, B.Sc. 

3. A Chemical Examination of the Organic Matter in Oil-Shales. By John B. Robertson, 
M.A., B.Sc. Communicated by Dr J. S. Flett, F.R.S. ( With Lantern Illustrations.) 

Mr William Fraser signed the Roll, and was duly admitted a Fellow of the Society. 



TENTH ORDINARY MEETING. 

Monday , May 4, 1914. 

Professor James Geikie, LL.D., D.C.L., F.R.S. , F.G.S., President, in the Chair. 

The following Communications were read : — 

1. Description and Exhibition of a Four-Dimensional Model. By Dr D. M. Y. Sommervtlle. 

2. Changes of Electrical Resistance accompanying Longitudinal and Transverse Magnetisations 
in Iron and Steel. By Dr C. G. Knott. 

3. Rocks from Gough Island, S. Atlantic : Scottish National Antarctic Expedition. By Dr 
Robert Campbell. Communicated by the President. ( With Lantern Illustrations.) 



ELEVENTH ORDINARY MEETING. 

Monday , May 25, 1914. 

Dr B. N. Peach, F’.R.S., Vice-President, in the Chair. 

The following Communications were read : — 

1. On the Inheritance of Certain Characters of the Wool of Sheep. By A. D. Darbishire, 
M.A., and Mr M. W. Gray. {With Lantern Illustrations.) 

2. On a New Species of Sclerocheilus, with a Revision of the Genus. By Dr J. H, Ashworth. 



TWELFTH ORDINARY MEETING. 

Monday, June 1, 1914. 

Professor James Geikie, LL.D., D.C.L., F.R.S,, F.G.S., President, in the Chair. 

The Council awarded : — 

1. The Neill Prize for the biennial period 1911-1912, 1912-1913 to William Speirs Bruce, 
LL. D. , in recognition of the scientific results of his Arctic and Antarctic explorations. 

2. The Keith Prize for the biennial period 1911-1912, 1912-1913 to Mr James Russell, 
for his series of investigations relating to magnetic phenomena in metals and the molecular theory 
of magnetism, the results of which have been published in the Proceedings and Transactions of 
the Society, the last paper having been issued within the period. 

The above prizes will be presented at the Ordinary Meeting on July 6, 1914. 

The following Communications were read : — 

1. The Analytical Study of the Mechanism of Writing. By James Dreyer, M.A., B.Sc. 
Communicated by Dr Alexander Morgan. ( With Exhibition of Apparatus and Lantern 
Illustrations. ) 

2. The Pinna-Trace in the Ferns. By R. C. Davie, M.A., B.Sc. Communicated by Professor 
Isaac Bayley Balfour, F.R.S. ( With Lantern Illustrations.) 

3. Abnormal Echinoids in the Collection of the Royal Scottish Museum. By Dr James 
Ritchie and James A. Todd, M.A. , B.Sc. Communicated by William Eagle Clarke. ( With 
Lantern Illustrations. ) 

The following signed the roll, and were admitted Fellows of the Society : Dr J. W. Pare, Dr 
Alex. C. Cumming, Mr James B. Ritchie, Mr Basil A. Pilkington, and Mr Theodore E. 
Salyesen. 



310 Proceedings of the Royal Society of Edinburgh. [Sess. 



THIRTEENTH ORDINARY MEETING. 

Monday , June 15, 1914. 

Professor James Geikie, LL.D., D.C.L., F.R.S., F.G.S., President, in the Chair. 

The following Communications were read : — 

1. Obituary Notice of Albert C. L. G. Gunther, M.A., M.D., Ph.D., F.R.S. By Professor 
W. C. MTntosh, F.R.S. 

2. The Fossil Osmundacese, Part V. By Dr R. Kidston, F.R.S. , F.G.S., and Professor 
D. T. Gwynne-Yaughan, M.A. ( With Lantern Illustrations.) 

3. The Hall and the Transverse Thermomagnetic Effects and their Temperature Coefficients. 
By F. Unwin, M.Sc. Communicated by Professor F. G. Baily. ( With Lantern Illustrations.) 

4. Some Factorable Continuants. By Professor W. H. Metzler, Ph.D. 

5. Atlantic Sponges collected by the Scottish National Antarctic Expedition. By Miss Jane 
Stephens. Communicated by Dr W. S. Bruce. 

The following Candidates for Fellowship were balloted for, and duly declared elected : — 
Alexander Gibb, A.M.Inst.C.E., and Robert Durward Clarkson, B.Sc., M.D., F.R.C.P.E. 
Mr Peter Ramsay signed the Roll, and was duly admitted a Fellow of the Society. 



FOURTEENTH ORDINARY MEETING. 

Monday , July 6, 1914. 

Professor James Geikie, LL.D., D.C.L., F.R.S., F.G.S., President, in the Chair. 

The following Prizes were presented : — 

1. The Neill Prize for the biennial period 1911-1912, 1912-1913 to William Speirs 
Bruce, LL.D., in recognition of the scientific results of his Arctic and Antarctic explorations. 

2. The Keith Prize for the biennial period 1911-1912, 1912-1913 to Mr James Russell, for 
his series of investigations relating to magnetic phenomena in metals and the molecular theory of 
magnetism, the results of which have been published in the Proceedings and Transactions of the 
Society, the last paper having been issued within the period. 

Neill Prize Award, 1911-13. 

The Neill Prize for the period 1911-1913 is awarded to Dr W. S. Bruce, a distinguished 
traveller and naturalist. Dr Bruce, as the Fellows of the Royal Society of Edinburgh well know, 
has spent his life in the exploration of Arctic and Antarctic seas and lands. He began his work 
more than twenty years ago by a voyage to certain islands of the Antarctic Ocean ; in recent 
years he has especially explored the Archipelago of Spitzbergen ; and in 1902 to 1904 he led the 
Scottish National Antarctic Expedition through its adventurous voyage to a successful issue. 

Dr Bruce’s many voyages, and especially the expedition of the Scotia , have led to the 
advancement of knowledge in many departments of science. With the science of geography itself, 
with the actual survey of new lands and seas, other Societies than this are peculiarly concerned. 
But as far as living memory goes back, the Royal Society of Edinburgh has been proud to 
encourage, with all its sympathy, and to help with all the means in its power, those discoveries, 
biological and physical, which follow and reward the explorations of the scientific traveller. 

In the Transactions of our Society there have appeared, during several recent years, a long 
series of papers based on the results of the Scotia Expedition ; in which papers new organisms 
from almost every group of the Animal Kingdom have been described, and in which important 
questions of physics, of meteorology, and of oceanography have been discussed. These many 
writings, by many hands, bear witness to the wisdom with which a great expedition was planned, 
to the enthusiasm with which its leader animated his band of men, and to the foresight and untiring 
industry which watched for and laid hold of the opportunities of discovery. 

Keith Prize Award, 1911-13. 

Mr Russell’s work, published mainly in our Transactions , dates from the early years of the 
century. In his first paper he discussed the problem of magnetic shielding in hollow iron 
cylinders, distinguishing the cases in which a transverse field existed alone, or had superposed 
upon it either a circular or a longitudinal field. This work was experimental, but its results were 
compared with those of the usual approximate theory. An investigation was also given of the 
inductions produced by mutually perpendicular fields, and the effects were co-ordinated for the 
first time and shown to be consistent with the results of the theory of molecular magnetism. 



311 



1913-14.] Meetings of the Society. 

Phenomena were discussed with regard to which considerable difference of opinion existed, and 
decisive results were obtained. 

Mr Russell’s work was next directed to an investigation of the effect of an oscillating magnetic 
field upon iron magnetised by a non-oscillating-field, and a careful discrimination was made, 
for the first time, between the cases in which the former field was first established, or conversely. 
Co-directed and perpendicularly directed fields were used, in the latter case possible disturbances 
due to the establishment of the oscillating field by means of a current flowing in the iron itself 
being for the first time avoided. Interesting and important results were obtained, and were 
applied to the formation of new views regarding the action of certain magnetic detectors used in 
wireless telegraphy. 

The preceding investigation led to a similar one in which mechanical vibrations were employed, 
and Mr Russell’s anticipation that similar results would be obtained was verified. Iron, nickel, 
and steel were investigated, both in the annealed and the tempered conditions, and general 
conclusions were obtained, while other interesting problems were suggested. 

One fact — the dependence of the neutral point in a hysteresis loop upon the intensity of the 
vibrational disturbance — was further investigated in a subsequent paper, and the apparently 
discordant results of other observers were harmonised. In a connected investigation on the effect 
of load and vibration upon magnetism in nickel, Mr Russell supplemented work of Ewing and 
Chree, upon iron and cobalt respectively, published in the Philosophical Transactions , and 
established the existence of a “ cyclic ” Yillari reversal. 

Mr Russell is an experimenter of great skill and resource. A visit to his private laboratory 
reveals how one man can do the work of three. And he is an accurate and acute reasoner. In 
his lengthy series of experimental inquiries, he has co-ordinated old, disconnected, or even 
seemingly discordant results, and has established new facts and new views. Throughout his 
whole work his aim has been to co-ordinate and explain highly complicated phenomena as the 
very direct results of the ideas of the molecular theory of magnetism based upon a simple view, 
given in his first paper, of the structural condition of a magnetic metal demagnetised by decreasing 
reversals. This is most noticeable in his latest paper which was communicated within the period 
of the present award. When the theory of magnetism in a medium crystallised on the cubic 
system is extended to an averagely random collocation of crystals, Mr Russell’s work will, with 
other work, form a touchstone. 

The following Communications were read 

1. Obituary Notice of John Sturgeon MacKay, M.A., LL.D. By Dr George Philip, 
George Watson’s College. 

2. Temperature Observations in Loch Earn. — Part II. By E. M. Wedderburn, D.Sc., and 
A. W. Young, M.A. {With Lantern Illustrations.) 

3. Contributions to the Geology of South Georgia. By D. Ferguson, M.I.M.E., with reports 
based on his collections by Professor J. W. Gregory, D.Sc., F.R.S., and G. W. Tyrrell, 
A.R.C.Sc., F.G.S. {With Lantern Illustrations.) 

The following Candidates for Fellowship were balloted for, and duly declared elected : — 

Alfred Frank Tredgold, L.R.C.P., M.R.C.S. , Hon. Consulting Physician to National 
Association for the Feebleminded; Francis John Lewis, D.Sc., F.L.S., Professor of Biology, 
University of Alberta ; Archibald M‘Kendrick, F.R.C.S.E., D.P.H., L.D.S. 



312 



Proceedings of the Royal Society of Edinburgh. 



PROCEEDINGS OF THE STATUTORY GENERAL MEETING 
Ending the 131st Session, 1913-1914. 



At the Annual Statutory Meeting of the Royal Society of Edinburgh, held in the Society’s 
Lecture Room, 24 George Street, on Monday i October 26, 1914, at 4.30 p.m., 

Professor James Geikie, President, in the Chair, 

the Minutes of the last Statutory Meeting, October 27, 1913, were read, approved, and signed. 

On the motion of Dr Knott, seconded by Dr Horne, Dr J. R. Milne and Mr A. G. 
Burgess were appointed Scrutineers, and the ballot for the New Council commenced. 

The General Secretary announced that the Council had granted leave of absence to Mr G. A. 
Stewart, Librarian, and Mr W. J. Beaton, Assistant Librarian, so as to enable them to join 
His Majesty’s forces. The Council had also felt it advisable to close the Society’s Rooms on 
Saturdays at one o’clock. 

The Treasurer’s Accounts for the past year, 1913-1914, were submitted. 

Professor Bower moved the approval of the Treasurer’s Report, and also votes of thanks to the 
Treasurer and the Auditors, who were. reappointed. This was agreed to. 



The Scrutineers reported that the following Council had been duly elected : — 



Professor James Geikie, LL.D., D.C.L., F.R.S., F.G.S., President. 
Professor T. Hudson Beare, M.Inst.C.E., \ 

Professor F. 0. Bower, M.A. , D.Sc., F.R.S., 

Professor Sir Thomas R. Fraser, M.D., LL.D., 



F.R.C.P.E., F.R.S., 

Benjamin N. Peach, LL.D., F.R.S., F.G. S. , 

Professor Sir E. A. Schafer, M.R.C.S., LL.D., F.R.S 
The Right Hon. Sir J. H. A. Macdonald, K.C. B 
P.C., LL.D., D.L., F.R.S., M.Inst.E.E., 

Cargill G. Knott, D.Sc., General Secretary. 

Robert Kidston, LL.D., F.R.S., F.G.S., 

Professor Arthur Robinson, M.D., M.R.C.S., 

James Currie, M.A. , Treasurer. 

John S. Black, M.A., LL.D., Curator of Library and Museum. 



> Vice-Presidents. 



j Secretaries to Ordinary 
I Meetings. 



ORDINARY MEMBERS OF COUNCIL. 



James Gordon Gray, D.Sc. 

Professor R. A. Sampson, M.A., D.Sc., F.R.S. 
Professor D’Arcy W. Thompson, C.B., B.A., 
F.L.S. 

Professor E. T. Whittaker, Sc.D., F.R.S. 
Principal A. P. Laurie, M.A., D.Sc. 

Professor J. Graham Kerr, M.A., F.R.S. 



Leonard Dobbin, Ph.D. 

Ernest Maclagan Wedderburn, M.A., 
LL.B. 

W. B. Blaikie, LL.D. 

John Horne, LL.D., F.S.S., F.G.S. 

R. Stewart MacDougall, M.A., D.Sc. 

W. A. Tait, D.Sc., M.Inst.C.E. 



SOOi ^o4 eP H“T™s°t: } W— Allan Ca KTEE , M.InstC.E. 



Abstract of Accounts. 



313 



ABSTRACT 

OF 



THE ACCOUNTS OF JAMES CURRIE, ESQ. 

As Treasurer of the Royal Society of Edinburgh. 

SESSION 1913-1914. 



I. ACCOUNT OF THE GENERAL FUND. 

CHARGE. 



1. Arrears of Contributions at 1st October 1913 ....... £106 1 0 

2. Contributions for present Session : — 

1. 141 Fellows at £2, 2s. each ...... £296 2 0 

127 Fellows at £3, 3s. each ...... 400 1 0 



£696 3 0 

Less — Subscription for present Session, included in 

1913 Accounts ...... 330 



£693 0 0 

2. Fees of Admission and Contributions of eleven new 

Resident Fellows at £5, 5s. each . . . . . 57 15 0 

3. Fees of Admission of eight new Non-Resident Fellows at 

£26, 5s. each 210 0 0 

4. Commutation Fees in lieu of future Contributions of two 

Fellows ......... 45 3 0 



3. Contribution for 1914-1915 paid in advance 

4. Interest received — 

Interest, less Tax £23, 4s. 10^d. . . £369 1 7 

Annuity from Edinburgh and District Water Trust, less 

Tax £3, 2s. 2d 49 7 10 

5. Transactions and Proceedings sold ..... ... 

6. Annual Grant from Government . ...... . 

7. Income Tax repaid for year to 5th April 1914 ...... 



1005 18 0 

2 2 0 



418 9 5 
140 1 1 

600 0 0 
25 18 11 



Amount of the Charge 



£2298 10 5 



DISCHARGE. 

1. Taxes, Insurance, Coal and Lighting 

Inhabited House Duty ...... 

Insurance ....... 

Coal, etc., to 24th August 1914 .... 

Gas to 12th March 1914 ..... 

Electric Light to 18th September 1914 . 

Water 1913-14 ..... 



£063 
9 0 9 

20 18 6 
0 4 10 

7 19 8 
4 4 0 

£42 14 0 



Carry forward 



£42 14 0 



314 



Proceedings of the Royal Society of Edinburgh. 



2. Salaries 

General Secretary . 
Librarian 

Assistant Librarian 
Office Keeper 
Treasurer’s Clerk . 



3. Expenses of Transactions : — 

Neill & Co., Ltd., Printers . 

Do. (for illustrations) 

M'Farlane & Erskine, Lithographers 
Hislop & Day, Engravers 
Orrock & Son, Bookbinders 
John Fowler & Co., Engravers 
Alex. Ritchie & Son, Lithographers 

4. Expenses of Proceedings : — 

Neill & Co., Ltd., Printers 

Do. (for illustrations) 

Hislop & Day, Engravers 
Alex. Ritchie & Son, Lithographers 
M‘Farlane & Erskine do. 

5. Books, Periodicals, Newspapers, etc."": — 

Otto Schulze & Co., Booksellers 
James Thin, do. 

R. Grant & Son, do. 

W. Green & Son, Ltd., do. 

International Catalogue of Scientific Literatui 
Robertson & Scott, News Agents . 

Egypt Exploration Funds Subscription . 

Ray Society do. 

Palseontographical Society do. 

Orrock & Son, Bookbinders . 

T. & A. Constable, Printers . 



Brought forward 



£42 14 0 



6. Expenses in Connection with Napier Tercentenary Reception : 
E. Sawers, Purveyor 
H. Dambmaun .... 

Gillies & Wright, Joiners 
A. Coutie & Son, do. 

G. Waterston & Sons, Ltd., Stationers 
Tait & Francis, Florists 
Attendants, Extra Cleaning, Posts, etc. 



7. Other Payments : — 

Neill & Co. , Ltd., Printers . 

E. Sawers, Purveyor ..... 
S. Duncan, Tailor (uniforms) 

Lantern Exhibitions, etc. , at Lectures . 
Lindsay, Jamieson & Haldane, C.A., Auditors 
Post Office Telephone Rent . 

A. Cowan & Sons, Ltd. . 

G. Waterston & Sons, Ltd. 

Gillies & Wright, Joiners 
R. Graham, Slater 
Mackenzie & Moncur, Ltd. 

Oliver Typewriter Co. , Ltd. 

Burn Bros., Plumbers . 

Petty Expenses, Postages, Carriage, etc. 



8. Interest Paid on Borrowed Money : — 

Makerstoun Magnetic Meteorological Observation Fund 



£100 


0 


0 


120 


0 


0 


49 


3 


4 


86 


14 


0 


25 


0 


0 


£430 


10 


11 


2 


16 


0 


109 


0 


6 


6 


18 


2 


108 


11 


0 


8 


9 


0 


44 


3 


0 


£281 


13 


7 


1 


1 


0 


12 


4 


9 


9 


0 


0 


2 


10 


0 


£109 


15 


8 


64 


0 


9 


7 


6 


. 4 


1 


8 


6 


17 


0 


0 


2 


0 


6 


4 


4 


0 


1 


1 


0 


1 


1 


0 


24 


6 


6 


0 


16 


0 


EPTION : - 






£15 


2 


4 


6 


5 


0 


5 


7 


10 


4 


10 


0 


3 


18 


6 


1 


10 


0 


3 


12 


6 


£68 


5 


0 


35 


17 


10 


11 


18 


0 


10 


10 


0 


6 


6 


0 


10 


0 


0 


10 


9 


6 


6 


16 


6 


21 


16 


8 


8 


5 


4 


2 


16 


3 


24 


6 


0 


2 


7 


3 


89 


8 


2 



380 17 4 



710 8 7 



306 9 4 



233 0 3 



40 6 2 



309 2 6 



5 5 2 



Carry forward 



£2028 3 4 



Abstract of Accounts. 



315 



Brought forward 

9. Irrecoverable Arrears of Contributions written off 
10. Arrears of Contributions outstanding at 1st October 1914 : — 
Present Session ......... 

Previous Sessions ......... 



. £2028 3 4 

2 2 0 

£59 17 0 
61 19 0 

121 16 0 



Amount of the Discharge 

Amount of the Charge 

Amount of the Discharge ........ 

Excess of Receipts over Payments for 1913-1914 

Deduct Floating Balance due by the Society at 1st October 1913 . 

Eloating Balance in favour of the Society at 1st October 1914 

Being — 

Balance due by Union Bank of Scotland, Ltd., on Account 



Current 
Balance in hands of Librarian 



Deduct Loan from the Makerstoun Magnetic Observation Fund 



£237 5 



£2152 1 4 

£2298 10 5 
2152 1 4 
£146 9 1 

123 16 2 

£22 12 11 



£243 11 
220 18 



£22 12 11 



II. ACCOUNT OF THE KEITH FUND 

To 1st October 1914. 

CHARGE. 

1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 



1st October 1913 ............ £62 10 7 

2. Interest Received 

On £896, 19s. Id. North British Railway Company 3 per cent. 

Debenture Stock for year to Whitsunday 1914, less Tax 

£1, 11s. lid. . . . £25 6 3 

On £211, 4s. North British Railway Company 3 per cent. Lien 

Stock for year to 30th June 1914, less Tax 7s. 7d. . 5 19 1 

31 5 4 

3. Income Tax repaid for year to 5 th April 1914 1188 



£95 14 7 



DISCHARGE. 

1. James Russell — Money Portion of Prize 1911-13 ...... £49 19 1 

2. Alexander Kirkwood & Son, Engravers, for Gold Medal . . . . 16 0 0 

3. Balance due by Union Bank of Scotland, Ltd., on Account Current at 

1st October 1914 ............ 29 15 6 



£95 14 7 



III. ACCOUNT OF THE NEILL FUND 

To ls£ October 1914. 

CHARGE. 

1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 

1st October 1913 ............ £49 3 0 

2. Interest Received : — 

On £355 London, Chatham and Dover Railway 4^ per cent. Arbitration 

Debenture Stock for year to 30th June 1914, less Tax 19s. 4d. . . . 15 0 2 

3. Income Tax repaid for year to 5 th April 1914. . . . . . 0188 



£65 1 10 



316 Proceedings of the Koyal Society of Edinburgh. 

DISCHARGE. 

1. Dr Wm. S. Bruce — Money Portion of Prize 1911-13 ...... £15 19 0 

2. Alexander Kirkwood & Son, Engravers, for- Gold Medal . . . . . 16 0 0 

3. Balance due by Union Bank of Scotland, Ltd., on Account Current at 

1st October 1914 33 2 10 



£65 1 10' 



IV. ACCOUNT OF THE MAKDOUGALL- BRISBANE FUND 

To 1st October 1914. 

CHARGE. 

1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 1st 

October 1913 £165 19 1 

2. Interest received 

On £365 Caledonian Railway Company 4 per cent. Consolidated Preference 

Stock No. 2 for year to 30th June 1914, less Tax 17s. 4d. . . . 13 14 8 

3. Income Tax repaid for year to 5th April 1914 ....... 0 17 0 



£180 10 0 

DISCHARGE. 

1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 

1st October 1914 £180 10 9' 



V. ACCOUNT OF THE MAKERSTOUN MAGNETIC METEOROLOGICAL 

OBSERVATION FUND 



To 1st October 1914. 
CHARGE. 



1. Balance due by General Fund at 1st October 1913 £220 13 6 

2. Interest received on Balances due by General Fund at Deposit Receipt Rates 

to 1st October 1914 552 



DISCHARGE. 

1. Donation to the Funds of the Napier Tercentenary Celebration . 

2. Balance due by General Fund at 1st October 1914 



£225 


18 


8 


£5 


0 


0 


220 


18 


8 


£225 


18 


8 



VI. ACCOUNT OF THE GUNNING VICTORIA JUBILEE PRIZE FUND 

To 1st October 1914. 

(Instituted by Dr R. H. Gunning of Edinburgh and Rio de Janeiro.) 

CHARGE. 

1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 1st 

October 1913 £41 15 4- 

2. Interest received on £1000 North British Railway Company 3 per cent. 

Consolidated Lien Stock for year to 30th June 1914, less Tax £1, 16s. 2d. . 28 3 10 

3. Income Tax repaid for year to 5th April 1914. 115 O' 



£71 14 2 



Abstract of Accounts. 



317 



DISCHARGE. 

1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 1st 

October 1914 £71 14 2 



STATE OF THE FUNDS BELONGING TO THE ROYAL 
SOCIETY OF EDINBURGH 



As at 1st October 1914. 

1. GENERAL FUND— 

1. £2090, 9s. 4d. three per cent. Lien Stock of the North British Railway 

Company at 75 per cent., the selling price at 1st October 1914 

2. £8519, 14s. 3d. three per cent. Debenture Stock of do. at 75 per cent., do. 

3. £52, 10s. Annuity of the Edinburgh and District Water Trust, equivalent 

to £875 at 154 per cent., do. ......... 

4. £1811 four per cent. Debenture Stock of the Caledonian Railway Company 

at 100| per cent., do. .......... 

5. £35 four and a half per cent. Arbitration Debenture Stock of the London, 

Chatham and Dover Railway Company at 106 \ per cent., do. . 

6. Arrears of Contributions, as per preceding Abstract of Accounts . 



£1567 17 0 
6389 15 8 

1347 10 0 

1820 1 1 

37 5 6 
121 16 0 



£11,284 5 3 



Add Floating Balance in favour of the Society, as per preceding Abstract 
of Accounts 



22 12 11 



Amount . . £11,306 18 2 



Exclusive of Library, Museum, Pictures, etc., Furniture of the Society’s Rooms at 
George Street, Edinburgh. 



2 . KEITH FUND— 

1. £896, 19s. Id. three per cent. Debenture Stock of the North British 

Railway Company at 75 per cent., the selling price at 1st October 1914 

2. £211, 4s. three per cent. Lien Stock of do. at 75 per cent., do. . 

3. Balance due by Union Bank of Scotland, Ltd., on Account Current . 

Amount 



£672 14 
158 8 

29 15 



£860 17 10 



3. NEILL FUND— 

1. £355 four and a half per cent. Arbitration Debenture Stock of the London, 

Chatham and Dover Railway Company at 106| percent., the selling price 

at 1st October 1914 £378 1 6 

2. Balance due by Union Bank of Scotland, Ltd., on Account Current . . 33 2 10 



Amount . . . £411 4 4 



4. MAKDOUGALL-BRISBANE FUND— 

1. £365 four per cent. Consolidated Preference Stock No. 2 of the Caledonian 

Railway Company at 94| per cent., the selling price at 1st October 1914 £344 18 6 

2. Balance due by Union Bank of Scotland, Ltd., on Account Current . . 180 10 9 



Amount . . . £525 9 3 



5. MAKERSTOUN MAGNETIC METEOROLOGICAL OBSERVATION FUND— 

Balance due by General Fund at 1st October 1914 ..... £220 18 8 



318 



Proceedings of the Royal Society of Edinburgh. 

6. GUNNING VICTORIA JUBILEE PRIZE FUND — Instituted by Dr Gunning of Edinburgh 
and Rio de Janeiro — 

1. £1000 three per cent. Consolidated Lien Stock of the North British Railway 

Company at 75 per cent., the selling price at 1st October 1914 . . £750 0 0 

2. Balance due by Union Bank of Scotland, Ltd. , on Account Current 71 14 2 



Amount . . £821 14 2 



Edinburgh, 15^ October 1914. — We have examined the six preceding Accounts of the 
Treasurer of the Royal Society of Edinburgh for the Session 1913-1914, and have found them to be 
correct. The securities of the various Investments at 1st October 1914, as noted in the foregoing 
Statement of Funds, have been exhibited to us. 



LINDSAY, JAMIESON & HALDANE, C.A., 

Auditors. 



Council of the Society. 



319 



THE COUNCIL OF THE SOCIETY, 

January 1915. 



President. 

JAMES GEIKIE, LL.D., D.C.L., F.R.S., F.G.S., Professor of Geology in the 
University of Edinburgh. 

V ice-Presidents. 

T. HUDSON BEARE, M.Inst.C.E., Professor of Engineering in the University of Edinburgh. 
FREDERICK 0. BOWER, M.A., D.Sc., F.R.S., F.L.S., Regius Professor of Botany in the 
University of Glasgow. 

Sir THOMAS R. FRASER, M.D., LL.D., Sc.D., F.R.C.P.E., F.R.S., Professor of Materia 
Medica in the University of Edinburgh. 

BENJAMIN N. PEACH, LL.D., F.R.S., F.G.S., formerly District Superintendent and Acting 
Palaeontologist of the Geological Survey of Scotland. 

Sir EDWARD ALBERT SCHAFER, M.R.C.S., LL.D., F.R.S., Professor of Physiology in the 
University of Edinburgh. 

The Right Hon. Sir J. H. A. MACDONALD, P.C., K.C., K.C.B., F.R.S., M.InstE.E., 
Lord President of the Second Division of the Court of Session. 

General Secretary. 

CARGILL G. KNOTT, D.Sc., Lecturer on Applied Mathematics in the University of Edinburgh. 

Secretaries to Ordinary Meetings. 

ROBERT KIDSTON, LL.D., F.R.S., F.G.S. 

ARTHUR ROBINSON, M.D., M.R.C.S., Professor of Anatomy in the University of Edinburgh. 

Treasurer. 

JAMES CURRIE, M. A. 

Curator of Library and Museum. 

JOHN SUTHERLAND BLACK, M.A., LL.D. 



Councillors. 



JAMES GORDON GRAY, D.Sc., Lecturer on 
Physics in the University of Glasgow. 

RALPH A. SAMPSON, M. A., D.Sc., F.R.S., 
Astronomer Royal for Scotland, and Pro- 
fessor of Astronomy in the University of 
Edinburgh. 

D’ARCY W. THOMPSON, C.B., B.A., F.L.S., 
Professor of Natural History in the 
University College, Dundee. 

EDMUND T. WHITTAKER, Sc.D., F.R.S., 
Professor of Mathematics in the University 
of Edinburgh. 

A. P. LAURIE, M. A., D.Sc., Principal of the 
Heriot-Watt College, Edinburgh. 



JOHN GRAHAM KERR, M.A., F.R.S., Pro- 
fessor of Zoology in the University of 
Glasgow. 

LEONARD DOBBIN, Ph.D., Lecturer on 
Chemistry in the University of Edin- 
burgh. 

ERNEST MACLAGAN WEDDERBURN, 
M.A., LL.B. , W.S., D.Sc. 

W. B. BLAIKIE, LL.D. 

JOHN HORNE, LL.D., F.R.S., F.G.S. 

R. STEWART MacDOUGALL, M.A., D.Sc. 

W. A. TAIT, D.Sc., M.Inst.C.E. 



By a Resolution of the Society, January 19, 1880, Principal Sir WILLIAM TURNER, 
K.C.B., D.C.L., F.R.S., having filled the office of President, is also a Member of Council. 



Society’s Representative on George Heriot’s Trust. 
WILLIAM ALLAN CARTER, M.Inst.C.E. 

Office, Library, etc., 22, 24 George Street, Edinburgh. Tel. No., 2881. 



320 



Proceedings of the Royal Society of Edinburgh. 



ALPHABETICAL LIST OF THE ORDINARY FELLOWS 
OF THE SOCIETY, 

Corrected to January 1, 1915. 



N.B . — Those marked * are Annual Contributors. 



B. prefixed to a name indicates that the Fellow has received a Makdougall-Brisbane Medal. 

K. .. ,, „ Keith Medal. 

N. ,, ,, ,, Neill Medal. 

Y. J. ,, „ ,, the Gunning Victoria Jubilee Prize. 

C. ,, ,, ,, contributed one or more Communications to the 

Society’s Transactions or Proceedings. 



Date of 
Election. 

1898 

1898 

1911 

1896 

1871 



C. 



1875 

1895 



C. K. 

v. j. 



1889 

1894 



1888 



C. 



1906 



1893 

1883 

1905 

1905 



1903 



1905 

1881 



C. 



1906 

1899 

1893 

1910 



C. 



1907 



1911 



C. 



* Abercromby, the Hon. John, LL.D., 62 Palmerston Place, Edinburgh 

Adami, Prof. J. G. , M.A. , M.D. Cantab., F.R.S., Professor of Pathology in M‘Gill 
University, Montreal 

* Adams, Archibald Campbell, A.M.Inst.Mech.E., A.M.Inst. E.E., Consulting 

Engineer, 1 Old Smithhills, Paisley 

* Affleck, Sir Jas. Ormiston, M.D., LL.D., F.R.C.P.E., 38 Heriot Row, Edinburgh 

Agnew, Sir Stair, K.C.B., M.A., formerly Registrar - General for Scotland,) 
22 Buckingham Terrace, Edinburgh 5 1 

Aitken, John, LL.D., F.R.S., Ardenlea, Falkirk 



Service on 
Council, etc. 



1882-85, 

1886-89, 

1891-93, 

1895-98. 



* Alford, Robert Gervase, M.Inst. C.E., Three Gables, Woodburn Park Road, Tun- 

bridge Wells, Kent 

Alison, John, M.A., Head Master, George Watson’s College, Edinburgh 
Allan, Francis John, M.D., C.M. Edin., M.O.H. City of Westminster, West- 
minster City Hall, Charing Cross Road, London 
Allardice, R. E., M.A., Professor of Mathematics in Stanford University, Palo 
Alto, Santa Clara Co. , California 10 

Anderson, Daniel E., M.D., B.A., B.Sc. f Green Bank, Merton Lane, Highgate, 
London, N. 

Anderson, J. Macvicar, Architect, 6 Stratton Street, London 
Anderson, Sir Robert Rowand, LL.D., 16 Rutland Square, Edinburgh 
Anderson, William, F.G.S., P. O. Box 635, Sydney, New South Wales, Australia 

* Anderson, William, M.A. , Head Science Master, George Watson’s College, Edin- 

burgh, 29 Lutton Place, Edinburgh 15 

Anderson-Berry, David, M.D. , LL.D., F.R.S.L., M.R.A.S., F.S.A. (Scot.), 
Versailles, Highgate, London, N. 

* Andrew, George, M. A. , B. A. , H. M. I. S. , Balwherrie, Strathearn Road, Broughty Ferry 
Anglin, A. H., M.A., LL.D., M.R.I.A., Professor of Mathematics, Queen’s 

College, Cork 

Appleton, Colonel Arthur Frederick, F.R.C.V.S., Nylstroom, Smoke Lane, Reigate 
Appleyard, James R., Royal Technical Institute, Salford, Manchester 20 

* Archer, Walter E., 17 Sloane Court, London, S.W. 

Archibald, E. H., B.Sc., Professor of Chemistry, Syracuse University, Syracuse, 
N.Y., U.S.A. 

* Archibald, James, M.A., Head Master, St Bernard’s School, 1 Leamington Terrace, 

Edinburgh 

* Ashworth, James Hartley, D.Sc., Lecturer on Invertebrate Zoology, University of 

Edinburgh, 4 Cluny Terrace, Edinburgh 

Badre, Muhammad, Ph.D., Almuneerah, Cairo, Egypt 25 I 



1912-14. 



1907 



Date of 

Electior 

1896 

1877 

1905 

1892 

1902 

1889 

1886 

1883 

1910 

1903 

1914 

1882 

1904 

1874 

1887 

1895 

1904 

1913 

1888 

1897 

1892 

1893 

1882 

1887 

1906 

1900 

1887 

1893 

1897 

1904 

1880 

1907 

1884 

1897 

1904 

1898 

1894 

1872 

1886 



Alphabetical List of the Ordinary Fellows of the Society. 



321 



* Baily, Francis Gibson, M.A., M.Inst.E.E. , Professor of Electrical Engineering, 

Heriot-Watt College, Edinburgh, Newbury, Colinton, Midlothian 
Balfour, I. Bayley, M.A., Sc.D., M.D., LL.D., F.R.S., F.L.S., King’s Botanist 
in Scotland, Professor of Botany in the University of Edinburgh and Keeper 
of the Royal Botanic Garden, Inverleith House, Edinburgh 
Balfour-Browne, William Alexander Francis, M.A., Barrister-at-Law, 26 Barton 
Road, Cambridge 

* Ballantyne, J. W. , M.D., F.R.C. P.E., 19 Rothesay Terrace, Edinburgh 

Bannerman, W. B., C.S.I., M.D., D.Sc., Surgeon General, Indian 

Medical Service, Madras, India 30 

Barbour, A. H. F., M.A., M.D., LL.D., F.R.C.P.E., 4 Charlotte Square, Edinburgh 
Barclay, A. J. Gunion, M.A., 729 Great Western Road, Glasgow 
Barclay, G. W. W., M.A., Raeden House, Aberdeen 

* Barclay, Lewis Bennett, C.E., 13 Cargill Terrace, Edinburgh 

Bardswell, Noel Dean, M.D., M.R.C.P. Ed. and Lond. , King Edward VII. Sana- 
torium, Midhurst 35 

* Barkla, Charles Glover, D.Sc. , F.R.S. , Professor of Natural Philosophy in the 

University of Edinburgh, Littledene, 34 Priestfield Road, Edinburgh 
Barnes, Henry, M. D., LL.D., 6 Portland Square, Carlisle 
Barr, Sir James, M.D., LL.D., F.R.C. P. Lond., 72 Rodney Street, Liverpool 
Barrett, Sir William F., F.R.S., M.R.I.A., formerly Professor of Physics, Royal 
College of Science, Dublin, 6 De Vesci Terrace, Kingstown, County Dublin 
Bartholomew, J. G., LL.D., F.R. G.S., The Geographical Institute, Duncan 
Street, Edinburgh 40 

Barton, Edwin H., D.Sc., A. M.Inst.E.E., Fellow Physical Society of London, 
Professor of Experimental Physics, University College, Nottingham 

* Baxter, William Muirhead, Glenalmond, Sciennes Gardens, Edinburgh 

Beard, Joseph, F.R.C.S. (Edin.), M.R.C.S. (Eng.), L.R.C.P. (Lond.), D.P.H. 
(Camb.), Medical Officer of Health and School Medical Officer, City of Carlisle, 
15 Brunswick Street, Carlisle 

Beare, Thomas Hudson, B.Sc., M.Inst.C.E., Professor of Engineering in the 
University of Edinburgh (Vice-President) 

* Beattie, John Carruthers, D.Sc., Professor of Physics, South African College, 

Cape Town 45 

Beck, Sir J. H. Meiting, Kt., M.D., M.R.C.P.E., Drostdy, Tulbagli, Cape 
Province, South Africa 

* Becker, Ludwig, Ph.D., Regius Professor of Astronomy in the University of 

Glasgow, The Observatory, Glasgow 

Beddard, Frank E., M.A. Oxon., F.R.S. , Prosector to the Zoological Society of 
London, Zoological Society’s Gardens, Regent’s Park, London 
Begg, Ferdinand Faithfull, 5 Whittington Avenue, London, E.C. 

Bell, John Patrick Fair, F.Z.S., Fulforth, Witton Gilbert, Durham 50 

* Bennett, James Bower, C.E., 5 Hill Street, Edinburgh 
Bernard, J. Mackay, ofDunsinnan, B.Sc., Dunsinnan, Perth 

* Berry, George A., M.D., C.M., F.R.C.S., 31 Drumsheugh Gardens, Edinburgh 
Berry, Richard J. A., M.D. , F.R.C.S.E., Professor of Anatomy in the University 

of Melbourne, Victoria, Australia 

*■ Beveridge, Erskine, LL.D., St Leonards Hill, Dunfermline 55 

Birch, De Burgh, C.B. , M. D., Professor of Physiology in the University of Leeds, 
8 Osborne Terrace, Leeds 

t Black, Frederick Alexander, Solicitor, 59 Academy Street, Inverness 

Black, John S., M.A., LL.D. (Curator of Library and Museum), 6 Oxford J 
Terrace, Edinburgh J 

Blaikie, Walter Biggar, LL.D., The Loan, Colinton 
: Bles, Edward J., M.A. , D.Sc., Elterholm, Cambridge 60 

' Blyth, Benjamin Hall, M.A., V.P.Inst.C. E., 17 Palmerston Place, Edinburgh 
Bolton, Herbert, M.Sc., F.G.S., F.Z.S., Director of the Bristol Museum and Art 
Gallery, Bristol 

Bottomley, J. Thomson, M.A., D.Sc., LL.D., F.R.S., F.C.S., 13 University 
Gardens, Glasgow 

Bower, Frederick O., M.A. , D.Sc., F.R.S., F.L.S., Regius Professor of Botany ( 
in the University of Glasgow, 1 St John’s Terrace, Hillhead, Glasgow J 
(Vice-President) i 

XIV. 



Service on 
Council, etc. 

1909-12. 



1888-91. 



1909-12. 



1907-1909. 

V-P 

1909- 



1891-94. 

Cur. 

1906- 

1914— 



1887-90, 

1893-96, 

1907-09. 

V-P 

1910- 

21 



322 

Date of 

Election. 

1884 

1901 

1903 

1886 

1907 

1912 

1895 

1893 

1901 

1907 

1864 

1913 

1898 

1911 

1883 

1885 

1909 

1912 

1906 

1898 

1870 

1887 

1905 

1902 

1894 

1887 

1888 

1896 

1887 

1897 

1910 

1893 

1894 

1905 

1904 



Proceedings of the Koyal Society of Edinburgh. 



Service on 
Council, etc. 



Bowman, Frederick Hungerford, D.Sc. , F.C.S. (Lond. and Berl.), F.I.C., 
A.Inst.C.E., A.Inst.M.E., M.Inst.E. E., etc., 4 Albert Square, Manchester 65 
Bradbury, J. B., M.D., Downing Professor of Medicine, University of 

Cambridge 

* Bradley, 0. Charnock, M.D., D.Sc., Principal, Royal Veterinary College, 

Edinburgh 

Bramwell, Byrom, M.D., F. R.C.P.E., LL.D. , 23 Drumsheugh Gardens, Edinburgh 

* Bramwell, Edwin, M.B., F.R.C.P.E., F.R.C.P. Lond., 24 Walker Street, Edin- 

burgh 

Bridger, Adolphus Edward, M.D. (Edin.), F.R.C.P. (Edin.), B.Sc. (Paris), B.L. 

(Paris), Foley Lodge, Langham Street, London, W. 70 

Bright, Charles, M. Inst.C.E., M.Inst.E. E., F.R.A.S., F.G.S., Consulting 

Engineer to the Commonwealth of Australia, The Grange, Leigh, Kent, and 
Members’ Mansions, Victoria Street, London, S.W. 

Brock, G. Sandison, M.D., 6 Corso d’ltalia, Rome, Italy 

* Brodie, W. Brodie, M.B., Thaxted, Dunmow, Essex 

Brown, Alexander, M.A., B.Sc., Professor of Applied Mathematics, South African 
College, Cape Town 



Brown, Alex. Crum, M.A., M.D., D.Sc., F.R.C.P.E., LL.D., F.R.S., Emeritus 
Professor of Chemistry in the University of Edinburgh, 8 Belgrave Crescent," 
Edinburgh 75 



* Brown, Alexander Russell, M.A., B.Sc., Science Master, Buckhaven Junior 

Student Centre, Norfield, Buckhaven 

* Brown, David, F.C.S., F.I.C., J.P., Willowbrae House, Willowbrae Road, 

Edinburgh 

* Brown, David Rainy, Chemical Manufacturer (J. F. Macfarlan & Co.), 

93 Abbeyhill, Edinburgh 

Brown, J. J. Graham, M.D., F.R.C.P.E., 3 Chester Street, Edinburgh 
Brown, J. Macdonald, M.D., F.R.C.S., 64 Upper Berkeley Street, Portman 
Square, London, W. 80 

* Brownlee, John, M.A., M.D., D.Sc., Ruchill Hospital, Biisland Drive, 

Glasgow 

* Bruce, Alexander Ninian, D.Sc., M.D. , 8 Ainslie Place, Edinburgh 

* Bruce, William Speirs, LL.D., Director of the Scottish Oceanographical Laboratory, 

Edinburgh, Antarctica, Joppa, Midlothian 

* Bryce, T. H., M.A., M.D, (Edin.), Professor of Anatomy in the University of 

Glasgow, 2 The University, Glasgow 

Buchanan, John Young, M.A., F.R.S., 26 Norfolk Street, Park Lane, 

London, W. 85 

Buist, J. B., M.D., F.R.C.P.E., 1 Clifton Terrace, Edinburgh 
Bunting, Thomas Lowe, M.D., 27 Denton Road, Scotswood, Newcastle-on-Tyne 

* Burgess, A. G., M.A., Mathematical Master, Edinburgh Ladies’ College, 

64 Strathearn Road, Edinburgh 

* Burgess, James, C.I.E., LL.D., Hon. A.R.I.B.A., F.R.G.S., Hon. M. Imp. 

Russ. Archseol. Soc., and Amer. Or. Soc., M. Soc. Asiat. de Paris, 
M.R.A.S., IT. Corr. M. Batavian Soc. of Arts and Sciences, and Berlin Soc. 
Anthrop., H. Assoc. Finno-Ugrian Soc., 22 Seton Place, Edinburgh 
Burnet, Sir John James, Architect, 18 University Avenue, Hillhead, Glasgow 90 
Burns, Rev. T., D.D., F.S.A. Scot., Minister of Lady Glenorchy’s Parish Church, 
Croston Lodge, Chalmers Crescent, Edinburgh 

* Butters, J. W. , M.A., B.Sc., Rector of Ardrossan Academy 
Cadell, Henry Moubray, of Grange, B.Sc., Linlithgow 

* Caird, Robert, LL.D., Shipbuilder, Greenock 

* Calderwood, Rev. Robert Sibbald, Minister of Cambuslang, The Manse, Cambuslang, 

Lanarkshire 95 

Calderwood, W. L., Inspector of Salmon Fisheries of Scotland, South Bank, Canaan 
Lane, Edinburgh 

* Cameron, James Angus, M. D., Medical Officer of Health, Firhall, Nairn 
Cameron, John, M.D., D.Sc., M.R.C.S. Eng., Anatomy Department, Middlesex 

Hospital Medical School, London, W. 

* Campbell, Charles Duff, Scottish Liberal Club, Princes Street, Edinburgh 



1907-10. 

1890-93. 



1865-68, 

1869-72, 

1873-75, 

1876-78, 

1911-13. 

Sec. 

1879-1905. 

V-P 

1905-11. 



1909-12. 

1911-14. 

1878-81, 

1S84-86. 



1895-98. 

1899-1902. 

V-P 

1908-14. 



Date of 

Election. 

1899 

1910 

1905 

1901 

1905 

1898 

1898 

1908 

1882 

1899 

1912 

1874 

1891 

1911 

1903 

1909 

1913 

1875 

1904 

1904 

1888 

1904 

1909 

1886 

1872 

1894 

1891 

1905 

1914 

1911 

1908 

1875 

1907 

1903 

1887 

1870 

1886 



Alphabetical List of the Ordinary Fellows of the Society. 



323 



c. 

c. 



c. 



y. j. 

c, 

o. 



* Carlier, Edmund W. W., M.D., M.Sc., F.E.S., Professor of Physiology, University, 

Birmingham 100 

Carnegie, David, M.Inst.C.E., M.Inst.Mech.E., M.I.S. Inst., 33-35 Charterhouse 
Square, London, E.C. 

* Carse, George Alexander, M. A., D. Sc. , Lecturer on Natural Philosophy, University 

of Edinburgh, 3 Middleby Street, Edinburgh 
Carslaw, H. S. , M.A., D.Sc. , Professor of Mathematics in the University of 
Sydney, New South Wales 

Carter, Joseph Henry, F.R.C.V.S., Stone House, Church Street, Burnley, 
Lancashire 

* Carter, Wm. Allan, M.Inst.C.E., 32 Great King Street, Edinburgh (Society’s 

Representative on George Heriot’s Trust) 105 

Carus- Wilson, Cecil, F.R.G.S., F.G.S., Waldegrave Park, Strawberry Hill, 
Middlesex, and Sandacres Lodge, Parkston e-on-Sea, Dorset 
Cavanagh, Thomas Francis, M.D., The Hospital, Bella Coola, B.C., Canada 
Cay, W. Dyce, M.Inst.C.E., 39 Victoria Street, Westminster, London 
Chatham, James, Actuary, 7 Belgrave Crescent, Edinburgh 

Chaudhuri, Banawari Lai, B.A.(Cal. ), B.Sc. (Edin.), Assistant Superintendent, 
Natural History Section, Indian Museum, 120 Lower Circular Road, Calcutta, 
India 110 

Chiene, John, C.B., M.D., LL.D., F.R.C.S.E., Emeritus Professor of Surgery in 
the University of Edinburgh, Barnton Avenue, Davidson’s Mains 

* Clark, John B., M.A. , Head Master of Heriot’s Hospital School, Lauriston, 

Garleffin, Craiglea Drive, Edinburgh 

* Clark, William Inglis, D.Sc., 29 Lauder Boad, Edinburgh 

* Clarke, William Eagle, F.L.S., Keeper of the Natural History Collections in the 

Royal Scottish Museum, Edinburgh, 35 Braid Road, Edinburgh 
Clayton, Thomas Morrison, M.D. , D.Hy., B.Sc., D.P. H., Medical Officer of 
Health, Gateshead, 13 The Crescent, Gateshead-on-Tyne 115 

* Cleghorn, Alexander, M.Inst.C.E., Marine Engineer, 14 Hatfield Drive, Kelvinside, 

Glasgow 

Clouston, Sir T. S., M.D., LL.D., F.R.C.P.E., 26 Heriot Row, Edinburgh 
Coker, Ernest George, M.A., D.Sc., Professor of Mechanical Engineering and 
Applied Mechanics, City and Guilds Technical College, Finsbury, Leonard 
Street, City Road, London, E.C. 

Coles, Alfred Charles, M. D., D.Sc., York House, Poole Road, Bourne- 
mouth, W. 

Collie, John Norman, Ph.D., D.Sc., LL.D., F.R.S., F.C.S., F.I.C., F.R.G.S., 
Professor of Organic Chemistry in the University College, Gower Street, 
London 120 

* Colquhoun, Walter, M.A. , M. B., 18 Walmer Crescent, Ibrox, Glasgow 

* Comrie, Peter, M.A., B.Sc., Head Mathematical Master, Boroughmuir Junior 

Student Centre, 1 9 Craighouse Terrace, Edinburgh 
Connan, Daniel M., M.A. 

Constable, Archibald, LL.D., 11 Thistle Street, Edinburgh 

Cook, John, M.A. , LL.D., formerly Principal, Central College, Bangalore, Director 
of Meteorology in Mysore, and Fellow, University of Madras, India, 9 Cobden 
Crescent, Edinburgh 125 

*' Cooper, Charles A., LL.D., 41 Drumsheugh Gardens, Edinburgh 

* Corrie, David, F.C.S., Nobel’s Explosives Company, Polmont, Stirlingshire 

* Coutts, William Barron, M.A. , B.Sc., 33 Dalhousie Terrace, Edinburgh 

* Cowan, Alexander C., Papermaker, Valleyfield House, Penicuik, Midlothian 
Craig, James Ireland, M. A., B. A. , Controller of the Department of General Statistics, 

14 Abdin Street, Cairo : The Koubbeh Gardens, near Cairo, Egypt 130 

Craig, William, M.D. , F.R.C.S. E. , Lecturer on Materia Medica to the College of 
Surgeons, 71 Bruntsfield Place, Edinburgh 

* Cramer, William, Ph.D., Lecturer in Physiological Chemistry in the University of 

Edinburgh, Physiological Department, The University, Edinburgh 
Crawford, Lawrence, M.A., D.Sc., Professor of Mathematics in the South African 
College, Cape Town 

Crawford, William Caldwell, 1 Lockharton Gardens, Colinton Road, Edinburgh 
Crichton-Browne, Sir Jas., M.D., LL.D., D.Sc., F.R.S., Lord Chancellor’s Visitor 
and Vice-President and Treasurer of the Royal Institution of Great Britain, 45 
Hans Place, S.W., and Royal Courts of Justice, Strand, London 135 

Croom, Sir John Halliday, M. D., F.R.C.P.E., Professor of Midwifery in the 
University of Edinburgh, late President, Royal College of Surgeons, Edin- 
burgh, 25 Charlotte Square, Edinburgh 



Service on 
Council, etc. 



1911-14. 



1884-86, 

1904-06. 



324 

Date of 

Electior 

1914 

1898 

1904 

1885 

1912 

1884 

1894 

1869 

1905 

1906 

1904 

1884 

1888 

1876 

1885 

1897 

1904 

1881 

1867 

1905 

1882 

1901 

1866 

1910 

1908 

1901 

1904 

1903 

1892 

1899 

1906 

1893 

1904 

1904 

1875 

1913 

1906 

1897 

1884 

1879 

1902 



Proceedings of the Poyal Society of Edinburgh. 



* Cumming, Alexander Charles, D.Sc., Lecturer in Chemistry, University, Edin- 

burgh, 16 Kilmaurs Terrace, Edinburgh 

* Currie, James, M.A. Cantab. (Treasurer), Larkfield, Goldenacre, Edin- / 

burgh \ 

* Cuthbertson, John, Secretary, West of Scotland Agricultural College, 6 Charles 

Street, Kilmarnock 

Daniell, Alfred, M.A., LL.B. , D.Sc., Advocate, The Athenseum Club, Pall Mall, 
London 140 

* Darbishire, Arthur Dukinfield, M.A., Lecturer in Genetics at the University of 

Edinburgh 

Davy, R., F. R.C.S. Eng., Consulting Surgeon to Westminster Hospital, Burstone 
House, Bow, North Devon 

* Denny, Sir Archibald, Bart., LL.D., Cardross Park, Cardross, Dumbartonshire 
Dewar, Sir James, Kt., M.A., LL.D., D.C.L., D.Sc., F.R.S., V.P.C.S., Jacksonian 

Professor of Natural and Experimental Philosophy in the University of 
Cambridge, and Fullerian Professor of Chemistry at the Royal Institution of 
Great Britain, London 

* Dewar, James Campbell, C.A., 27 Douglas Crescent, Edinburgh 145 

'Dewar, Thomas William, M.D. , F.R.C.P., Kincairn, Dunblane 

Dickinson, Walter George Burnett, F.R.C.V.S., Boston, Lincolnshire 
Dickson, the Right Hon. Charles Scott, K. C., LL.D., 22 Moray Place, Edinburgh 
Dickson, Henry Newton, M.A., D.Sc., 160 Castle Hill, Reading 
Dickson, J. D. Hamilton, M.A. , Senior Fellow and formerly Tutor, St Peter’s 
College, Cambridge 150 

Dixon, James Main, M.A., Litt. Hum. Doctor, Professor of English, University 
of Southern California, Wesley Avenue, Los Angeles, California, U.S.A. 
Dobbie, James Bell, F.Z.S., 12 South Inverleith Avenue, Edinburgh 
Dobbie, Sir James Johnston, Kt., M.A., D.Sc., LL.D., F.R.S., Principal of the 
Government Laboratories, London. 4 Vicarage Gate, Kensington, London, W. 
Dobbin, Leonard, Ph. D., Lecturer on Chemistry in the University of Edinburgh, f 
6 Wilton Road, Edinburgh \ 

Donaldson, Sir James, M.A., LL.D., Principal of the University of St 
Andrews 155 

Donaldson, Rev. Wm. Galloway, F.R.G.S., F.E.I.S., The Manse, Forfar 
Dott, David B., F. I.C., Memb. Pharm. Soc., Ravenslea, Musselburgh 
Douglas, Carstairs Cumming, M.D., D.Sc., Professor of Medical Jurisprudence 
and Hygiene, Anderson’s College, Glasgow, 2 Royal Crescent, Glasgow 
Douglas, David, 22 Drummond Place, Edinburgh 

Douglas, Loudon MacQueen, Author and Lecturer, 3 Lauder Road, Edinburgh 160 
Drinkwater, Harry, M.D., M.R.C.S. (Eng.), F.L.S., Lister House, Wrexham, 

North Wales 

Drinkwater, Thomas W., L.R.C.P.E., L.R.C.S.E., Chemical Laboratory, Surgeons’ 
Hall, Edinburgh 

Dunlop, William Brown, M.A., 4a St Andrew Square, Edinburgh 
Dunstan, John, M.R. C.V.S., Inversnaid, Liskeard, Cornwall 
Dunstan, M. J. R., M.A., F. I.C., F.C.S., Principal, South-Eastern Agricultural 
College, Wye, Kent 165 

Dutliie, George, M.A. , Inspector-General of Education, Salisbury, Rhodesia 
Dyson, Sir Frank Watson, Kt., M.A., LL.D., F.R.S., Astronomer Royal, Royal 
Observatory, Greenwich 
Edington, Alexander, M. D., Howick, Natal 
Edwards, John, 4 Great Western Terrace, Kelvinside, Glasgow 
Elder, William, M.D., F.R.C.P.E., 4 John’s Place, Leith 170 

Elliot, Daniel G. , American Museum of Natural History, Central Park West, 
New York, N.Y., U.S.A. 

Elliot, George Francis Scott, M.A. (Cantab.), B.Sc., F.R.G.S., F.L.S., Drumwhill, 
Mossdale 

Ellis, David, D.Sc., Ph.D., Lecturer in Botany and Bacteriology, Glasgow and 
West of Scotland Technical College, Glasgow 
Erskine- Murray, James Robert, D.Sc., 4 Great Winchester Street, London, E.C. 
Evans, William, F.F.A., 38 Morningside Park, Edinburgh 175 

Ewart, James Cossar, M.D., F.R.C.S.E., F.R.S., F.Z.S., Regius Professor off 
Natural History, University of Edinburgh, Craigybield, Penicuik, Mid--J 
lothian I 

Ewen, John Taylor, B.Sc., M.I.Mech.E., H.M. Inspector of Schools, 104 King’s 
Gate Aberdeen 



Service on 
Council, etc. 



Treas. 

1906- 



1872-74. 



1905-08. 

1904-07 

1913- 

1870-78. 



1907-10. 



1882-85, 

1904-07. 

V-P 

1907-12. 



Date of 

Election. 

1878 

1900 

1910 

1875 

1907 

1888 

1883 

1899 

1907 

1904 

1888 

1898 

1899 

1911 

1906 

1900 

1872 

1904 

1892 

1910 

1896 

1867 

1914 

1891 

1891 

1907 

1888 

1901 

1899 

1867 

1909 

1880 

1861 



Alphabetical List of the Ordinary Fellows of the Society. 



Ewing, Sir James Alfred, K.C.B., M.A., B.Sc., LL.D., M.Inst.C.E., F.R.S., 
Director of Naval Education, Admiralty, Froghole, Edenbridge, Kent 
Eyre, John W. H., M. D. , M.S. (Dunelm), D.P. H. (Camb. ), Guy’s Hospital 
(Bacteriological Department), London 

* Fairgrieve, Mungo M'Callum, M.A. (Glasg.), M. A. (Cambridge), Master at the 

Edinburgh Academy, 37 Queen’s Crescent, Edinburgh 180 

Fairley, Thomas, Lecturer on Chemistry, 8 Newton Grove, Leeds 
Falconer, John Downie, M.A., D.Sc., F.G.S., Lecturer on Geography, The 
University, Glasgow. 

Fawsitt, Charles A., Coney Park, Bridge of Allan 

Felkin, Robert W. , M. D., F.R. G.S., 47 Bassett Road, North Kensington, 
London, W. 

* Fergus, Andrew Freeland, M.D. , 22 Blythswood Square, Glasgow 185 

* Fergus, Edward Oswald, 12 Clairmont Gardens, Glasgow 

* Ferguson, James Haig, M.D., F.R.C.P.E., F.R.C.S.E., 7 Coates Crescent, 

Edinburgh 

Ferguson, John, M.A., LL.D., Professor of Chemistry in the University of 
Glasgow 

* Findlay, John R., M.A. Oxon., 27 Drumsheugh Gardens, Edinburgh 

* Finlay, David W., B.A., M.D. , LL.D. , F.R.C.P., D.P.H., Emeritus Professor of 

Medicine in the University of Aberdeen, Honorary Physician to His Majesty 
in Scotland, 23 Dundonald Road, Glasgow, W. 190 

Fleming, John Arnold, F.C.S., etc., Pottery Manufacturer, Woodburn, Rutherglen, 
Glasgow 

* Fleming, Robert Alexander, M.A. , M.D. , F.R. C.P.E. , Assistant Physician, Royal 

Infirmary, 10 Chester Street, Edinburgh 

* Flett, John S., M.A., D.Sc., LL.D., F.R.S., Director of the Geological Survey of 

Scotland, 33 George Square, Edinburgh 

Forbes, Professor George, M.A., M.Inst.C.E., M.Inst.E.E., F.R.S., F.R.A.S., 
11 Little College Street, Westminster, S.W. 

Forbes, Norman Hay, F.R.C.S.E. , L.R.C.P. Lond., M.R.C.S. Eng., Corres. 
Memb. Soc. d’Hydrologie medicale de Paris, Druminnor, Church Stretton, 
Salop 195 

* Ford, John Simpson, F.C.S., 4 Nile Grove, Edinburgh 

* Fraser, Alexander, Actuary, 17 Eildon Street, Edinburgh 

* Fraser, John, M.B., F.R. C.P.E., formerly one of H.M. Commissioners in 

Lunacy for Scotland, 54 Great King Street, Edinburgh 

Fraser, Sir Thomas R., Kt., M.D., LL.D., Sc.D., F.R. C.P.E., F.R.S., Professor 
of Materia Medica in the University of Edinburgh, Honorary Physician to J 
the King in Scotland, 13 Drumsheugh Gardens, Edinburgh. (Vice- 
President) 

* Fraser, William, Managing Director, Neill & Co., Ltd., Printers, 17 Eildon Street, 

Edinburgh 200 

* Fullarton, J. H., M.A., D.Sc., 23 Porchester Gardens, London, W. 

* Fulton, T. Wemyss, M.D. , Scientific Superintendent, Scottish Fishery Board, 

41 Queen’s Road, Aberdeen 

* Galbraith, Alexander, Superintendent Engineer, Cunard Line, Liverpool, 93 

Trinity Road, Bootle, Liverpool 

Galt, Alexander, D.Sc., Keeper of the Technological Department, Royal Scottish 
Museum, Edinburgh 

Ganguli, Sanjiban, M.A., Principal, Maharaja’s College, and Director of Public 
Instruction, Jaipur State, Jaipur, India 205 

Gatehouse, T. E., A.M. Inst.C.E., M.Inst.M.E., M.Inst.E.E.. Fairfield, 128 Tulse 
Hill, London, S.W. 

Gayner, Charles, M.D., F.L.S. 

* Geddes, Auckland C., M.D. , Professor of Anatomy, M'Gill University, Montreal, 

Canada 

Geddes, Patrick, Professor of Botany in University College, Dundee, and Lecturer 
on Zoology, Ramsay Garden, University Hall, Edinburgh 
Geikie, Sir Archibald, O.M., K.C.B., D.C.L. Oxf., D.Sc., LL.D., Ph.D., Late Pres. 
R.S., Foreign Member of the Reale Accad. Lincei, Rome, of the National Acad, 
of the United States, of the Academies of Stockholm, Christiania, Gottingen, 
Corresponding Member of the Institute of France and of the Academies of 
Berlin, Vienna, Munich, Turin, Belgium, Philadelphia, New York, etc., 
Shepherd’s Down, Haslemere, Surrey 210 



325 



Service on 
Council, etc. 

1888-91. 



1870-73, 

1877-79, 

1883-86, 

1894-97. 

V-P 

1911- 



1869-72, 

1874-76, 

1879-82. 



326 

Date of 

Election. 

1871 

1914 

1909 

1914 

1910 

1912 

1910 

1890 

1911 

1900 

1880 

1907 

1909 

1911 

1898 

1910 

1901 

1899 

1913 

1897 

1891 

1898 

1883 

1910 

1909 

1910 

1886 

1897 

1905 

1906 

1905 

1910 

1899 

1907 



Proceedings of the Royal Society of Edinburgh. 



Geikie, James, LL. D. , D.C.L., F.R. S., F. G.S., formerly Professor of Geology 
in the University of Edinburgh (President), Kilmorie, Colinton Road,- 
Edinburgh 

Gemmell, John Edward, M.B., C.M., Hon. Surgeon Hospital for Women and 
Maternity Hospital ; Hon. Gynaecologist, Victoria Central Hospital, Liscard, 
28 Rodney Street, Liverpool. 

* Gentle, William, B.Sc., 12 Mayfield Road, Edinburgh 

* Gibb, Alexander, A.M. Inst.C. E., St Martin’s Abbey, by Perth 

* Gibb, David, M.A., B.Sc., Lecturer in Mathematics, Edinburgh University, 

15 South Lauder Road, Edinburgh 215 

* Gibson, Arnold Hartley, D.Sc., Professor of Engineering, University College, Dundee 

* Gibson, Charles Robert, Lynton, Mansewood, by Pollokshaws 

Gibson, George A., M.A., LL.D., Professor of Mathematics in the University of j 
Glasgow, 10 The University, Glasgow \ 

Gidney, Henry A. J. , L.M. and S. Socts. Ap. (Lond.), F.R.C.S. (Edin.), D.P.H. 
(Camb.), D.O. (Oxford), Army Specialist Public Health, c/o Thomas Cook & 
Sons, Ludgate Circus, London 

Gilchrist, Douglas A., B.Sc., Professor of Agriculture and Rural Economy, 
Armstrong College, Newcastle-upon-Tyne 220 

Gil ruth, Ueorge Ritchie, Surgeon, 53 Northumberland Street, Edinburgh 
Gilruth, John Anderson, M-.R.C.V.S., D.V.Sc. (Melb.), Administrator, Govern- 
ment House, Darwin Northern Territory, Australia 

* Gladstone, Hugh Steuart, M.A., M.B.O.U., F.Z.S., 40 Lennox Gardens, London, 

S.W. 

Gladstone, Reginald John, M.D., F.R.C.S. (Eng.), Lecturer on Embryology and 
Senior Demonstrator of Anatomy, Middlesex Hospital, London, 22 Regent’s 
Park Terrace, London, N.W. 

* Glaister, John, M.D., F.R.F.P.S. Glasgow, D.P.H. Camb. , Professor of Forensic 

Medicine in the University of Glasgow, 3 Newton Place, Glasgow 225 

Goodall, Joseph Strickland, M.B. (Lond.), M.S.A. (Eng.), Lecturer on Physiology, 
Middlesex Hospital, London, Annandale Lodge, Vanbrugh Park, Blackheath, 
London, S.E. 

Goodwillie, James, M.A., B.Sc., Liberton, Edinburgh 
’‘'Goodwin, Thomas S., M.B., C.M., F.C.S., 25 Worple Road, Isleworth, and 
Derwent Lodge, London Road, Spring-grove, Isleworth, Middlesex 

* Gordon, William Thomas, M.A., D.Sc. (Edin.), B.A. (Cantab.), Lecturer in 

Geology, University of London, King’s College, Strand, W.C. 

Gordon-Munn, John Gordon, M.D., Heigham Hall, Norwich 230 

* Graham, Richard D., 11 Strathearn Road, Edinburgh 
*Gray, Albert A., M.D., 4 Clairmont Gardens, Glasgow 

Gray, Andrew, M.A., LL.D., F.R.S., Professor of Natural Philosophy in the J 
University of Glasgow 

Gray, Bruce M ‘Gregor, C.E., A.M. Inst.C. E., Westbourne Grove, Selby, York- 
shire 

* Gray, James Gordon, D.Sc., Lecturer in Physics in the University of Glasgow, 11 

The University,. Glasgow 235 

* Green, Charles Edward, Publisher, Gracemount House, Liberton 

Greenfield, W. S. , M.D., F.R.C. 1 J . E. , LL.D., Emeritus Professor of General 
Pathology in the University of Edinburgh, Kirkbrae, Elie, Fife 
Greenlees, Thomas Duncan, M.D. Edin., Rostrevor, Kirtleton Avenue, Weymouth, 
Dorset 

* Gregory, John Walter, D.Sc., F. R. S. ; Professor of Geology in the University of 

Glasgow, 4 Park Quadrant, Glasgow 

Greig, Edward David Wilson, M.D., B.Sc., Captain, H.M. Indian Medical 
Service, BycullaClub, Bombay, India 240 

Greig, Robert Blyth, LL.D., F.Z.S., Board of Agriculture for Scotland, 29 St 
Andrew Square, Edinburgh 

* Grimshaw, Percy Hall, Assistant Keeper, Natural History Department, The Royal 

Scottish Museum, 49 Comiston Drive, Edinburgh 

* Guest, Edward Graham, M.A., B.Sc., 5 Newbattle Terrace, Edinburgh 

* Gulliver, Gilbert Henry, D.Sc., A.M.I.Mech.E., 99 Southwark Street, London, 

S.E. 



Service on 
Council, etc. 

1882-85, 

1888-91, 

1897-99. 

V-P 

1892-97. 
1900-05. 
P. 1913- 



1905-08. 

1912-13. 



1903-06. 

V-P 

1906-09. 



1913- 



1908-11. 



Date of 

Election. 

"l911 

1883 

1911 

1910 

1911 

1905 

1899 

1876 

1896 

1914 

1888 

1869 

1914 

1881 

1880 

1892 

1893 

1890 

1900 

1908 

1890 

1881 

1908 

1894 

1902 

1904 

1885 

1911 

1881 

1896 

1904 

1897 

1912 

1893 



Alphabetical List of the Ordinary Fellows of the Society. 



* Gunn, James Andrew, M. A., M.D., D.Sc., Department of Pharmacology, University 

Museum, Oxford 245 

Guppy. Henry Brougham, M. B., Rosario, Salcombe, Devon 

* Guy, William, F.R. C.S. , L.R.C.P. , L.D.S. Ed., Consulting Dental Surgeon, Edin- 

burgh Royal Infirmary ; Dean, Edinburgh Dental Hospital and School ; 
Lecturer on Human and Comparative Dental Anatomy and Physiology, 11 
Wemyss Place, Edinburgh 

Gwynne- Vaughan, D. T., F.L.S., Professor of Botany, 14 London Road, 
Reading 

Hall-Edwards, John Francis, L.R.C.P. (Edin.), Hon. F.R.P.S., Senior Medical 
Officer in charge of X-ray Department, General Hospital, Birmingham, 
141 a and 141 b Great Charles Street (Newliall Street), Birmingham 

* Halm, Jacob E. , Ph.D. , Chief Assistant Astronomer, Royal Observatory, Cape] 

Town, Cape of Good Hope 250 

Hamilton, Allan M‘Lane, M.D., LL.D., 36 East 40th Street, New York, U.S.A. 
Hannay, J. Ballantyne, Sorbie, 10 Balgillo Terrace, Broughty Ferry 

* Harris, David Fraser, B.Sc. (Lond.), D.Sc. (Birm. ), M. D. , F. S.A. Scot., Professor 

of Physiology in the Dalhousie University, Halifax, Nova Scotia 
Harrison, Edward Philip, Ph.D., Professor of Physics, Presidency College, Uni- 
versity of Calcutta, The Observatory, Alipore, Calcutta 
Hart, D. Berry, M.D., F.R. C.P.E. , 5 Randolph Cliff, Edinburgh 255 

Hartley, Sir Charles A., K.C.M.G., M.Inst.C.E., 26 Pall Mall, London 
Harvey- Gibson, Robert John, M.A., F. L.S., D.L. for the County Palatine of 
Lancaster, M. R.S.G.S. , Professor of Botany, University of Liverpool, 22 
Falkner Square, Liverpool 

Harvie-Brown, J. A., of Quarter, LL.D., F.Z.S., Dunipace House, Larbert, 
Stirlingshire 

Haycraft, J. Berry, M.D., D.Sc., Professor of Physiology in the University College 
of South Wales and Monmouthshire, Cardiff 

* Heath, Thomas, B.A., formerly Assistant Astronomer, Royal Observatory, Edin- 

burgh, 11 Cluny Drive, Edinburgh 260 

Hehir, Patrick, M. D. , F.R.C.S.E. , M.R.C.S., L.R.C. P.E., Surgeon -Captain, 
Indian Medical Service, Principal Medical Officer, H.H. the Nizam’s Army, 
Hyderabad, Deccan, India 

Helme, T. Arthur, M.D., M.R.C.P., M.R.C.S., 3 St Peter’s Square, Manchester 
Henderson, John, D.Sc., A. Inst.E.E., Kinnoul, Warwick’s Bench Road, Guild- 
ford, Surrey 

* Henderson, William Dawson, M.A. , B.Sc., Ph.D., Lecturer, Zoological Laboratories, 

University, Bristol 

Hepburn, David, M. D., Professor of Anatomy in the University College of South 
Wales and Monmouthshire, Cardiff 265 

Herdman, W. A., D.Sc., F.R.S., Past Pres. L.S., Professor of Natural History in 
the University of Liverpool, Croxteth Lodge, Ullet Road, Liverpool 

* Hewat, Archibald, F.F.A., F.I.A., 13 Eton Terrace, Edinburgh 

Hill, Alfred, M.D. , M.R.C.S., F.I.C., Valentine Mount, Freshwater Bay, Isle of 
Wight 

* Hinxman, Lionel W., B.A., Geological Survey Office, 33 George Square, 

Edinburgh 

Hobday, Frederick T. G. , F. R.C.V. S., 6 Berkely Gardens, Kensington, 

London, W. 270 

Hodgkinson, W. R., Ph.D., F.I.C., F.C.S., Professor of Chemistry and Physics 
at the Ordnance College, Woolwich, 89 Shooter’s Hill Road, Blackheath, Kent 
Holland, William Jacob, LL.D. St Andrews, etc., Director Carnegie Institute, 
Pittsburg, Pa., 5545 Forbes Street, Pittsburg, Pa., U.S.A. 

Horne, John, LL.D., F.R.S., F.G.S., formerly Director of the Geological Survey _ 
of Scotland, 12 Keith Crescent, Blackhall, Midlothian 

Horne, J. Fletcher, M.D., F.R.C.S.E., The Poplars, Barnsley 

* Horsburgh, Ellice Martin, M.A. , B.Sc., Lecturer in Technical Mathematics, 

University of Edinburgh, 11 Granville Terrace, Edinburgh 275 

Houston, Alex. Cruikshanks, M.B., C. M., D.Sc., 19 Fairhazel Gardens, South 
Hampstead, London, N.W. 

* Houstoun, Robert Alexander, M.A. , Ph.D., D.Sc., Lecturer in Physical Optics, 

University, Glasgow, 11 Cambridge Drive, Glasgow 
Howden, Robert, M.A., M.B. , C.M., D.Sc., Professor of Anatomy in the University 
of Durham, 14 Burdon Terrace, Newcastle-on-Tyne 



327 



Service on 
Council, etc. 



1902-05, 

1906- 07. 
1914- 

V-P 

1907- 1913. 



328 

Date of 

Election. 

1899 

1883 

1910 

1886 

1911 

1887 

1887 

1908 

1912 

1904 

1904 

1914 

1875 

1894 

1889 

1901 

1912 

1906 

1900 

1895 

1903 

1874 

1905 

1888 

1907 

1912 

1909 

1908 

1903 

1891 

1913 

1908 

1886 

1907 

1880 

1883 

1878 



Proceedings of the Royal Society of Edinburgh. 



Howie, W. Lamond, F.C.S., 26 Neville Court, Abbey Road, Regent’s Park, 
London, N.W. 

Hoyle, William Evans, M.A., D.Sc., M.R.C.S., Director of the Welsh National 
Museum ; Crowland, Llandaff, Wales 280 

Hume, William Fraser, D.Sc. (Lond.), Director, Geological Survey of Egypt, 
Helwan, Egypt 

Hunt, Rev. H. G. Bona via, Mus.D. Dub., Mus.B. Oxon., The Yicarage, Burgess 
Hill, Sussex 

Hunter, Gilbert Macintyre, M.Inst.C.E., M.Inst.E.S., M.Inst.M.E., Resident 
Engineer Nitrate Railways, Iquique. Chile, and Maybole, Ayrshire 
Hunter, James, F.R.C.S.E., F.R.A.S., Rosetta, Liberton, Midlothian 
Hunter, William, M.D., M.R.C.P.L. and E. , M.R.C.S., 54 Harley Street, 
London 285 

Hyslop, Theophilus Bulkeley, M.D., M.R.C.P.E., 5 Portland Place, London, W. 

* Inglis, Robert John Mathieson, A.M.Inst. C.E., Engineer, Northern Division, 

North British Railway, Tantah, Peebles 
Innes, R. T. A., Director, Government Observatory, Johannesburg, Transvaal 

* Ireland, Alexander Scott, S.S.C., 2 Buckingham Terrace, Edinburgh 

Jack, John Noble, Professor of Agriculture to the County Council of Sussex, 
Kingscote, The Avenue, Lewes, Sussex 290 

Jack, William, M.A., LL.D. , Emeritus Professor of Mathematics in the University 
of Glasgow 

Jackson, Sir John, C.Y.O., LL.D., 48 Belgrave Square, London 
James, Alexander, M.D., F.R.C. P.E., 14 Randolph Crescent, Edinburgh 
*Jardine, Robert, M.D., M.R.C.S. F.R.F.P.S. Glas., 20 Royal Crescent, 
Glasgow 

* Jeffrey, George Rutherford, M.D. (Glasg.), F.R.C.P. (Edin.), etc., Bootham Park 

Private Mental Hospital, York 295 

* Jehu, Thomas James, M.A., M.D., F.G.S., Professor of Geology in the University 

of Edinburgh 

*Jerdan, David Smiles, M. A., D.Sc., Ph.D., Temora, Colinton, Midlothian 
Johnston, Col. Hemy Halcro, C.B., Late A.M.S., D.Sc., M.D., F.L.S., Orphir 
House, Kirkwall, Orkney 

* Johnston, Thomas Nicol, M.B., C.M., Pogbie, Humbie, East Lothian 

Jones, Francis, M.Sc. , Lecturer on Chemistry, 17 Whalley Road, Whalley Range, 
Manchester 300 

Jones, George William, M.A. , B.Sc. , LL. B., Scottish Tutorial Institute, 
Edinburgh and Glasgow, 25 North Bridge : Coraldene, Kirk Brae, Liberton, 
Edinburgh 

Jones, John Alfred, M.Inst.C.E., Fellow of the University of Madras, Sanitary 
Engineer to the Government of Madras, c/o Messrs Parry & Co., 70 Grace- 
church Street, London 

* Kemp, John, M.A. , Sea Bank School, North Berwick 

Kennedy, Robert Foster, M.D. (Queen’s Univ., Belfast), M.B., B.Ch. (R.U.I.), 
Assistant Professor of Neurology, Cornell University, New York, 20 West 
50th Street, New York, U.S.A. 

Kenwood, Henry Richard, M.B., Chadwick Professor of Hygiene in the University 
of London, 126 Queen’s Road, Finsbury Park, London, N. 305 

* Kerr, Andrew William, F.S.A. Scot., Royal Bank House, St Andrew Square, 

Edinburgh 

*Kerr, John Graham, M.A., F.R.S., Professor of Zoology in the University/ 
of Glasgow \ 

Kerr, Joshua Law, M.D., The Chequers, Mittagong, Sydney, Australia 

* Kerr, Walter Hume, M.A., B.Sc., Lecturer on Engineering Drawing and Structural 

Design in the University of Edinburgh 

Kidd, Walter Aubrey, M.D., 12 Montpelier Row, Blackheath, London 310 

Kidston, Robert, LL.D., F.R.S., F.G.S. (Secretary), 12 Clarendon Place, J 
Stirling 

* King, Archibald, M.A., B.Sc., formerly Rector of the Academy, Castle Douglas ; 

Junior Inspector of Schools, La Maisonnette, Clarkston, Glasgow 
King, W. F., Lonend, Russell Place, Trinity, Leith 

Kinnear, the Right Hon. Lord, P.C., one of the Senators of the College of Justice, 2 
Moray Place, Edinburgh 

Kintore, the Right Hon. the Earl of, P.C., G.C. M.G., M.A. Cantab., LL.D. 
Cambridge, Aberdeen and Adelaide, Keith Hall, Inverurie, Aberdeenshire 315 



Service on 
Council, etc. 



1888-91. 



1904-07, 

1913- 



1891-94, 

1903-06. 

Sec. 

1909- 



Alphabetical List of the Ordinary Fellows of the Society. 



329 



Date of 
Election. 

1901 

1907 

1880 

1886 

1878 

1910 

1885 

1894 

1910 

1905 

1910 

1903 

1874 

1910 

1914 

1905 

1889 

1912 

1912 

1903 

1903 

1898 

1884 

1888 

1900 

1894 

1887 

1907 

1883 

1903 
1905 
1397 

1904 

1886 



* Knight, Rev. G. A. Frank, M.A., 52 Sardinia Terrace, Hillhead, Glasgow 

* Knight, James, M.A., D.Sc., F.C.S., F.G.S., Head Master, St James’ School, 

Glasgow, The Shieling, Uddingston, by Glasgow 



!. K. 



Knott, C. G., D.Sc., Lecturer on Applied Mathematics in the University of 
Edinburgh (formerly Professor of Physics, Imperial University, Japan)-; 
(Gen. Secretary), 42 Upper Gray Street, Edinburgh 



C. 



C. 

c. 

c. 



c. 



!. K. 



c. 



Laing, Rev. George P. , 1 7 Buckingham Terrace, Edinburgh 

Lang, P.R. Scott, M.A., B.Sc., Professor of Mathematics, University of St Andrews 320 

* Lauder, Alexander, D.Sc., F. I.C., Lecturer in Agricultural Chemistry, Edinburgh 

and East of Scotland College of Agriculture, 13 George Square, Edinburgh 

Laurie, A. P., M.A., D.Sc., Principal of the Heriot-Watt College, Edinburgh | 

* Laurie, Malcolm, B.A., D.Sc., F.L.S., 19 Merchiston Park, Edinburgh 

* Lawson, A. Anstruther, B.Sc., Ph.D., D.Sc., F.L.S., Professor of Botany, Univer- 

sity of Sydney, New South Wales, Australia 

* Lawson, David, M.A. , M.D., L.R.C.P. and S.E., Druimdarroch, Banchory, 

Kincardineshire 325 

*Lee, Gabriel W., D.Sc., Palaeontologist, Geological Survey of Scotland, 33 George 
Square, Edinburgh 

* Leighton, Gerald Rowley, M.D., Local Government Board, 125 George Street, 

Edinburgh 

Letts, E. A., Ph.D., F.I.C., F.C.S., Professor of Chemistry, Queen’s College, Belfast 
Levie, Alexander, F.R.C.V.S., D.Y.S.M., Veterinary Surgeon, Lecturer on 
Veterinary Science, Veterinary Infirmary, 12 Derwent Street, Derby 
Lewis, Francis John, D.Sc., F. L.S., Professor of Biology, University of Alberta, 
Edmonton South, Alberta, Canada 330 

* Lightbody, Forrest Hay, 56 Queen Street, Edinburgh 

Lindsay, 'Rev. James, M.A., D.D., B.Sc., F.R.S.L., F.G.S., M.R.A.S., Corre- 
sponding Member of the Royal Academy of Sciences, Letters and Arts, of 
Padua, Associate of the Philosophical Society of Louvain, Annick Lodge, 
Irvine 

* Lindsay, John George, M.A., B.Sc. (Edin.), Science Master, Royal High School, 

33 Lauriston Gardens, Edinburgh 

* Linlithgow, The Most Honourable the Marquis of, Hopetoun House, South 

Queensferry 

Liston, William Glen, M.D., Captain, Indian Medical Service, c/o Grindlay. Groom 
& Co.. Bombay, India 335 

* Littlejohn, Henry Harvey, M.A., M.B., B.Sc., F.R.C.S.E., Professor of Forensic 

Medicine, Dean of the Faculty of Medicine in the University of Edinburgh, 
11 Rutland Street, Edinburgh 

* Lothian, Alexander Veitch, M.A. , B.Sc., Training College, Cowcaddens, Glasgow 
Low, George M., Actuary, 11 Moray Place, Edinburgh 

Lowe, D. F., M.A., LL.D. , formerly Head Master of Heriot’s Hospital School, 
Lauriston, 19 George Square, Edinburgh 
Lusk, Graham, Ph.D., M.A. , Professor of Physiology, Cornell University Medical 
College, New York, N.Y., U.S.A. 340 

* Mabbott, Walter John, M.A., Rector of County High School, Duns, Berwickshire 
M'Aldowie, Alexander M., M.D., Glengarriff, Leckhampton, Cheltenham 
MacAlister, Donald Alexander, A.R.S.M., F.G. S., 26 Thurloe Square, South 

Kensington, London, S.W. 

M‘Bride, P., M.D., F.R.C.P.E., 10 Park Avenue, Harrogate, and Hill House, 
Withy pool, Dunster, Somerset 

*M‘Cormick, Sir W. S., M.A., LL.D., Secretary to the Carnegie Trust for the 
Universities of Scotland, 13 Douglas Crescent, Edinburgh 345 

* Macdonald, Hector Munro, M. A., F.R.S., Professor of Mathematics, University of 

Aberdeen, 52 College Bounds, Aberdeen 

* Macdonald, James A., M.A., B.Sc., H.M. Inspector of Schools, Stewarton, 

Kilmacolm 

* Macdonald, John A., M.A., B.Sc., King Edward VII. School, Johannesburg, 

Macdonald, the Right Hon. Sir J. H. A. (Lord Kingsburgh) P.C., K.C., K.C.B., 
LL.D., F.R.S., M.Inst.E.E., Lord Justice- Clerk, and Lord President of the | 
Second Division of the Court of Session, 15 Abercromby Place, Edinburgh 



Service on 
Council, etc. 



1894-97, 

1898-01, 

1902-05. 

Sec. 

1905-1912. 
Gen. Sec. 
1912- 



1908-11, 

1913- 



1910-13. 

1908-11. 



1889-92. 



330 

Date of 
Election. 

1904 

1886 

1901 

1910 
1888 
1885 

1897 
1878 

1903 

1911 

1869 

1895 

1914 

1873 

1912 

1900 

1910 

1911 

1894 

1904 

1910 

1904 

1869 

1899 

1888 

1913 

1907 

1898 
1913 

1908 

1912 

1913 

1880 

1909 



Proceedings of the Poyal Society of Edinburgh. 



c. 

o. 

o. 



!. N. 
C. 

). B. 
0 . 



0 . 



c. 



0 . 

a 



c. 



c. 

c. 



Macdonald, William, B.Sc. , M. Sc. , Agriculturist, Editor Transvaal Agricultural 
Journal , Department of Agriculture, Pretoria Club, Pretoria, Transvaal 350 
Macdonald, William J., M.A., LL.D., 15 Comiston Drive, Edinburgh 

* MacDougall, R. Stewart, M.A., D.Sc., Professor of Biology, Royal Veterinary 

College, Edinburgh, 9 Dryden Place, Edinburgh 
Macewen, Hugh Allan, M. B., Ch.B., D.P. H. (Lond. and Camb.), Local 
Government Board, Whitehall, London, S.W. 

M'Fadyean, Sir John, M.B., B.Sc., LL.D., Principal, and Professor of Comparative 
Pathology in the Royal Veterinary College, Camden Town, London 
Macfarlane, J. M., D.Sc., Professor of Botany and Director of the Botanic Garden, 
University of Pennsylvania, Philadelphia, Pennsylvania, U.S.A. 355 

* MacGillivray, Angus, C.M., M.D., D.Sc., 23 South Tay Street, Dundee 
M'Gowan, George, F. I.C., Ph. D., 21 Montpelier Road, Ealing, Middlesex 

* MTntosh, Donald C. , M.A., D.Sc., 3 Glenisla Gardens, Edinburgh 

MTntosh, John William, A.R.C.V.S., 14 Templar Street, Myatts Park, 
London, S.E. 

MTntosh, William Carmichael, M.D., LL.D., F.R.S., F.L.S., Professor of Natural 
History in the University of St Andrews, Pres. Ray. Society, 2 Abbotsford 
Crescent, St Andrews 360 

* Macintyre, John, M.D., 179 Bath Street, Glasgow 

* M ‘Kendrick, Archibald, F.R.C.S.E., D.P.H., L.D.S., 2 Coates Place, Edinburgh 



M'Kendrick, John G. , M.D., F.R.C.P.E., LL.D., F.R.S., Emeritus Professor of^ 
Physiology in the University of Glasgow, Maxieburn, Stonehaven 



V 

M ‘Kendrick, Anderson Gray, M.B. , Major, Indian Medical Service, Officiating 
Statistical Officer to the Government of India, The Pasteur Institute, Kasauli, 
India 

*M‘Kendrick, John Souttar, M.D., F.R.F.P.S.G., 2 Buckingham Terrace, 
Glasgow 365 

* Mackenzie, Alister, M.A., M.D., D.P.H., Principal, College of Hygiene and 

Physical Training, Dunfermline 

* M‘Kenzie, Kenneth John, M. A., Master of Method to Leith School Board, 

24 Dudley Gardens, Leith 

* Mackenzie, Robert, M.D., Napier, Nairn 

* Mackenzie, W. Leslie, M.A., M.D., D.P.H., LL.D., Medical Member of the Local 

Government Board for Scotland, 4 Clarendon Crescent, Edinburgh 

* MacKinnon, James, M. A., Ph.D., Professor of Ecclesiastical History, Edinburgh 

University, 12 Lygon Road, Edinburgh 370 

* Mackintosh, Donald James, M.V.O., M.B., C.M., LL.D., Supt. Western Infirmary, 

Glasgow 

Maclagan, R. C., M.D., F.R.C.P.E., 5 Coates Crescent, Edinburgh 
Maclean, Ewan John, M. D., M.R.C.P. Lond., 12 Park Place, Cardiff 
Maclean, Magnus, M.A., D.Sc., M.Inst.E.E., Professor of Electrical Engineering 
in the Royal Technical College, 51 Kerrsiand Terrace, Hillhead, Glasgow 
*M‘Lellan, Dugald, M. Inst.C.E., District Engineer, Caledonian Railway, 42 
Ormidale Terrace, Murrayfield, Edinburgh 375 

* Macnair, Peter, Curator of the Natural History Collections in the Glasgow 

Museums, Kelvingrove Museum, Glasgow 
Mahalanobis, S. C., B.Sc., Professor of Physiology, Presidency College, Calcutta, 
India 

Majumdar, Tar ak Nath, D.P.H. (Cal.), L.M.S., F.C.S., Health Officer, Calcutta, 
IV., 37 Lower Chitpore Road, Calcutta, India 
Mallik, Devendranath, B.A., B.Sc., Professor of Physics and Mathematics, 
Patna College, Bankipur, Bengal, India 

Maloney, William Joseph, M.D.(Edin.), Professor of Neurology at Fordham 
University, New York City, N.Y., U.S.A. 380 

Marchant, Rev. James, F.R.A.S., Director, National Council for Promotion of 
Race- Regeneration ; Literary Adviser to House of Cassell ; 42 Great Russell 
Street, London, W.C. 

Marsden, R. Sydney, M.D., C.M., D.Sc., D.P.H., Hon. L.A.H. Dub., M.R.I.A., 
F.I.C. , M.O.H., Rowallan House, Cearns Road, and Town Hall, Birkenhead 

* Marshall, C. R. , M.D., M.A., Professor of Materia Medica and Therapeutics, 

Medical School, Dundee, Arnsheen, Westfield Terrace, West Newport, 
Fife 



Service on 
Council, etc. 



1914- 



1885-88. 



1875-78, 

1885-88, 

1893- 94, 
1900-02. 

V-P 

1894- 1900. 



Alphabetical List of the Ordinary Fellows of the Society. 



331 



Date of 
Election. 

1882 

1901 

1903 

1912 

1913 

1885 

1898 

1911 

1906 

1902 

1901 

1888 

1902 

1885 

1908 

1910 

1909 

1905 

1905 

1904 

1886 

1899 

1889 

1897 

1900 
1899 

1911 

1906 

1890 

1887 

1896 

1892 

1914 

1901 
1892 
1874 

1888 



C. 



c. 



0 . 

J. B. 



C. 

C. 

1 B. 



0 . 



0 . 



c. 

c. 

c. 



0 . 



c. 

!. K. 

C. 



Marshall, D. H., M.A., Professor, Union and Alwington Avenue, Kingston, 
Ontario, Canada 

* Marshall, F. H. A., Sc. D., Lecturer on Agricultural Physiology in the Uni- 

versity of Cambridge, Christ’s College, Cambridge 385 

^ Martin, Nicholas Henry, F.L.S., F.C.S., Ravenswood, Low Fell, Gateshead 

* Martin, Sir Thomas Carlaw, LL.D., J.P. , Director, Royal Scottish Museum, 

4 Gordon Terrace, Edinburgh 

Masson, George Henry, M.D., D.Sc., M.R.C.P.E., Port of Spain, Trinidad, 
British West Indies 

Masson, Orme, D. Sc. , F. R. S. , Professor of Chemistry in the University of Melbourne 

* Masterman, Arthur Thomas, M.A., D.Sc., Inspector of Fisheries, Board of 

Agriculture, Whitehall, London 390 

Mathews, Gregory Macalister, F.L.S., F.Z.S., Langley Mount, Watford, Herts 
*Mathieson, Robert, F. C.S. , Rillbank, Innerleithen 
Matthews, Ernest Romney, A. M.Inst. C.E., F.G.S., Chadwick Professor of 
Municipal Engineering in the University of London, University College, 
Gower Street, London, W.C. 

* Menzies, Alan W. C. , M.A. , B.Sc., Ph. D. , F.C.S., Professor of Chemistry, 

Princeton University, Princeton, New Jersey, U.S.A. 

Methven, Cathcart W., M.Inst.C.E., F.R.I.B.A., Durban, Natal, S. Africa 395 
Metzler, William H., A. B. , Ph.D. , Corresponding Fellow of the Royal Society 
of Canada, Professor of Mathematics, Svracuse University, Svracuse, N.Y., 
U.S.A. 

Mill, Hugh Robert, D.Sc., LL.D., 62 Camden Square, London 

* Miller, Alexander Cameron, M.D., F.S.A. Scot., Craig Linnlie, Fort-William, 

Inverness-shire 

* Miller, John, M.A., D.Sc., Professor of Mathematics, Royal Technical College, 

2 Northbank Terrace, North Kelvinside, Glasgow 
Mills, Bernard Langley, M.D., F.R.C.S.E., M.R.C.S., D.P.H., Lt.-Col. 

R. A. M.C., formerly Army Specialist in Hygiene, 84 Grange Crescent, Sharrow, 
Sheffield 400 

* Milne, Archibald, M.A., B.Sc., Lecturer on Mathematics and Science, Edinburgh 

Provincial Training College, 108 Comiston Drive, Edinburgh 

* Milne, C. H., M.A., Head Master, Daniel Stewart’s College, 4 Campbell Road, 

Mur ray field, Edinburgh 

* Milne, James Robert, D.Sc., Lecturer on Natural Philosophy, 11 Melville Crescent, 

Edinburgh 

Milne, William, M.A., B.Sc., 70 Beechgrove Terrace, Aberdeen 

* Milroy, T. H., M. I)., B.Sc., Professor of Physiology in Queen’s College, Belfast, 

Meloyne, Malone Park, Belfast 405 

Mitchell, A. Crichton, D.Sc., Hon. Doc. Sc. (Geneve), formerly Director of Public 
Instruction in Travancore, India, 103 Trinity Road, Edinburgh 
Mitchell, George Arthur, M.A., 9 Lowther Terrace, Kelvinside, Glasgow 

* Mitchell, James, M.A., B.Sc., Cruach, Lochgilphead 

* Mitchell-Thomson, Sir Mitchell, Bart., 6 Charlotte Square, Edinburgh 

Modi, Edalji Manekji, D.Sc., LL.D., Litt.D., F.C.S., etc., Proprietor and Director of 
Arthur Road Chemical Works, Meher Buildings, Tardeo, Bombay, India 410 
Moffat, Rev. Alexander, M.A., B.Sc., Professor of Physical Science, Christian 
College, Madras, India 

Mond, R. L., M.A. Cantab., F.C.S., Combe Bank, near Sevenoaks, Kent 
Moos, N. A. F. , L.C.E., B.Sc., Professor of Physics, Elphinstone College, and 
Director of the Government Observatory, Colaba, Bombay, India 

* Morgan, Alexander, M.A., D.Sc., Principal, Edinburgh Provincial Training 

College, 1 Midmar Gardens, Edinburgh 

Morrison, J. T., M.A., B.Sc., Professor of Physics and Chemistry, Victoria 
College, Stellenbosch, Cape Colony 415 

Mort, Spencer, M. D., Ch.B., F.R.C.S.E., Medical Superintendent, Edmonton 
Infirmary, London, N. 

Moses, O. St John, I.M.S., M.D., D.Sc., F.R.C.S., Captain, Professor of Medical 
Jurisprudence, 26 Park Street, Wellesley, Calcutta, India 
Mossman, Robert C. , Acting Editor, British Rainfall Organization’s Publications, 
63a Burntwood Lane, Wandsworth Common, London, S.W. 

Muir, Thomas, C.M.G., M.A. , LL.D., F.R.S., Superintendent-General of Educa- 
tion for Cape Colony, Education Office, Cape Town, and Mowbray Hall, 
Rosebank, Cape Colony 

Muirhead, George, Commissioner to His Grace the Duke of Richmond and Gordon, 
K.G., Spey bank, Fochabers , 420 I 



Service on 
Council, etc. 



1902-04. 



1885-88. 

V-P 

1888-91. 



332 

Date of 

Election. 

1907 

1887 

1891 

1896 

1907 

1907 

1902 

1888 

1897 

1906 

1898 

1884 

1880 

1878 

1906 

1888 

1888 

1886 

1895 

1914 

1908 

1905 

1914 

1892 

1901 

1886 

1892 

1881 

1907 

1914 

1904 

1889 

1887 

1893 

1913 

1889 

1907 

1914 



Proceedings of the Royal Society of Edinburgh. 



Muirhead, James M. P. , J.P., F. R.S.L. , F.S.S., c/o Dunlop Rubber Co., Ltd., 
3 Wallace Street, Fort, Bombay 

Mukhopadhyay, Asutosh, M.A., LL.D., F.R.A.S. , M.R.I.A., Professor of Mathe- 
matics at the Indian Association for the Cultivation of Science, 77 Russa 
Road North, Bhowanipore, Calcutta, India 

Munro, Robert, M.A., M.D., LL.D., Hon. Memb. R.I.A., Hon. Memb.J 
Royal Society of Antiquaries of Ireland, Elmbank, Largs, Ayrshire j 

Murray, Alfred A., M.A. , LL.B., 20 Warriston Crescent, Edinburgh 
' Murray, James, Hill Farm Bungalow, Froxfield, Hants 425 

Musgro.ve, James, M.D., F.R.C.S. Edin. and Eng., Bute Professor of Anatomy, 
University of St Andrews, The Swallowgate, St Andrews 
Mylne, Rev. R. S. , M.A., B.C. L. Oxford, F.S.A. Lond. , Great Amwell, Herts 
Napier, A. D. Leith, M.D., C.M., M.R.C.P., 28 Angas Street, Adelaide, 
S .A.fisti'ciliR 

Nash, Alfred George, B.Sc., F.R.G.S., C.E., Belretiro, Mandeville, Jamaica, W.I. 

* Newington, Frank A., M.Inst.C.E., M.Inst.E.E., 7 Wester Coates Road, Edin- 

burgh 430 

Newman, Sir George, M.D., D.P.H. Cambridge, Lecturer on Preventive Medicine, 
St Bartholomew’s Hospital, University of London : Grim’s Wood, Harrow 
Weald, Middlesex 

Nicholson, J. Shield, M.A., D.Sc., Professor of Political Economy in the) 
University of Edinburgh, 3 Belford Park, Edinburgh 1 

Nicol, W. W. J., M.A. , D.Sc., 15 Blacket Place, Edinburgh 

Norris, Richard, M.D., M.R.C.S. Eng., 3 Walsall Road, Birchfield, Birmingham 

* O’Connor, Henry, A. M.Inst.C.E., 1 Drummond Place, Edinburgh 435 

Ogilvie, F. Grant, C.B., M.A., B.Sc., LL.D., Secretary of the Board of Education 

for the Science Museum and the Geological Survey, and Director of the 
Science Museum, 15 Evelyn Gardens, London, S.W. 

Oliphant, James, M.A. , 11 Heathfield Park, Willesden Green, London 
Oliver, James, M.D., F.L.S., Physician to the London Hospital for Women, 
123 Harley Street, London, W. 

Oliver, Sir Thomas, M.D. , LL.D.. F. R.C.P., Professor of Physiology in the 
University of Durham, 7 Ellison Place, Newcastle-upon-Tyne 

* Oswald, Alfred, Lecturer in German, Glasgow Provincial Training College, 

Nordheim, Bearsden, Glasgow 440 

Page, William Davidge, F.C.S., F.G.S., M.Inst.M.E., 10 Clifton Dale, York 
Pallin, William Alfred, F.R. C.Y.S. , Major in the Army Veterinary Corps, 
c/o Messrs Holt & Co., 3 Whitehall Place, London 
Pare, John William, M.B., C.M., M.D., L.D.S., Lecturer in Dental Anatomy, 
National Dental Hospital, 64 Brook Street, Grosvenor Square, London, W. 
Parker, Thomas, M.Inst.C.E., Severn House, Iron Bridge, Salop 

* Paterson, David, F.C. S., Lea Bank, Rosslyn, Midlothian 445 



Paton, D. Noel, M.D., B.Sc., F.R.C.P.E., F.R.S. ; 
the University of Glasgow, University, Glasgow 



Professor of Physiology in 



Paulin, Sir David, Actuary, 6 Forres Street, Edinburgh 

Peach, Benjamin N., LL.D., F.R.S., F.G.S. (Vice-President), formerly District | 
Superintendent and Acting Palaeontologist of the Geological Survey of 4 
Scotland, 72 Grange Loan, Edinburgh 



* Pearce, John Thomson, B.A., B.Sc., School House, Tranent 

Pearson, Joseph, D.Sc., F.L.S., Director of the Colombo Museum, and Marine 
Biologist to the Ceylon Government, Colombo Museum, Ceylon 450 

* Peck, James Wallace, M.A., Chief Inspector, National Health Insurance, Scotland, 

83 Princes Street, Edinburgh 

Peck, William, F.R.A.S. , Town’s Astronomer, City Observatory, Calton Hill, 
Edinburgh 

Peddie, Wm. , D.Sc., Professor of Natural Philosophy in University College, 
Dundee, Rosemount, Forthill Road, Broughty Ferry 
Perkin, Arthur George, F.R.S., 8 Montpellier Terrace, Hyde Park, Leeds 

* Philip, Alexander, M.A. , LL.B., Writer, The Mary Acre, Brechin 455 

Philip, Sir R. W., M.A. , M. D., F.R.C.P.E., 45 Charlotte Square, Edinburgh 
Phillips, Charles E. S., Castle House, Shooter’s Hill, Kent 

* Pilkington, Basil Alexander, 20 Queen’s Avenue, Blackhall, Midlothian 



Service on 
Council, etc. 



1894-97, 

1900-03. 

V-P 

1903-08. 



1885-87, 

1892-95. 

1897-1900. 



1901-03. 



1894-97 

1904- 06, 
1909-12. 

1905- 08, 

1911- 1912. 
V-P 

1912- 



1904-07 

1908-11. 



Date of 

Election. 

1905 

1908 

1911 

1906 

1886 

1888 

1902 

1892 

1875 

1908 

1903 

1911 

1898 

1897 

1899 

1884 

1914 

1911 

1891 

1904 

1900 

1883 

1889 

1902 

1902 

1913 

1908 

1914 

1913 

1908 

1875 

1914 

1906 

1898 

1880 

1900 

1896 

1902 



Alphabetical List of the Ordinary Fellows of the Society. 



* Pinkerton, Peter, M.A., D.Sc., Rector, High School, Glasgow, 44 St James’s 

Street, Hillhead, Glasgow 

* Pirie, James Hunter Harvey, B. Sc. , M.D., F. R. C.P. E., Bacteriological Laboratory, 

Nairobi, British East Africa 460 

* Pirie, James Simpson, Civil Engineer, 28 Scotland Street, Edinburgh 
Pitchford, Herbert Watkins, F.R.C.V.S., Bacteriologist and Analyst, Natal 

Government, The Laboratory, Pietermaritzburg, Natal 
Pollock, Charles Frederick, M.D., F.R.C.S.E., 1 Buckingham Terrace, Hillhead, 
Glasgow 

Prain, Sir David, Lt.-Col., Indian Medical Service (Retired), C.M.G., C.I.E., M.A., 
M.B., LL.D., F. L.S., F.R.S., For. Memb. K. Svensk. Vetensk. Akad. ; Hon. 
Memb. Soc. Lett, ed Arti d. Zelanti, Acireale ; Pharm. Soc. Gt. Britain ; Corr. 
Memb. K. Bayer Akad. Wiss. , etc. ; Director, Royal Botanic Gardens, Kew, 
Surrey 

* Preller, Charles Du Riche, M.A., Ph.D., A.M.Inst.C.E., 61 Melville Street, 

Edinburgh 465 

* Pressland, Arthur J. , M. A. Camb. , Edinburgh Academy 
Prevost, E. W. , Ph.D., Weston, Ross, Herefordshire 

* Pringle, George Cossar, M.A. , Rector of Peebles Burgh and County High School, 

Bloomfield, Peebles 

* Pullar, Laurence, Dunbarney, Bridge of Earn, Perthshire 

Purdy, John Smith, M.D.,_ C.M. (Aberd.), D.P. H. (Camb.), F.R.G.S., Chief 
Health Officer for Tasmania, Islington, Hobart, Tasmania 470 

* Purves, John Archibald, D.Sc., 13 Albany Street, Edinburgh 

* Rainy, Harry, M.A., M.B., C.M., F.R.C.P. Ed., 16 Great Stuart Street, Edinburgh 

* Ramage, Alexander G., 8 Western Terrace, Murrayfield, Edinburgh 

Ramsay, E. Peirson, M.R. I.A. , F.L.S., C.M.Z.S. , F.R.G.S., F.G.S., Fellow of 
the Imperial and Royal Zoological and Botanical Society of Vienna, Curator 
of Australian Museum, Sydney, N. S. W. 

* Ramsay, Peter, M.A., B.Sc. , Head Mathematical Master, George Watson’s 

College, 63 Comiston Drive, Edinburgh 475 

* Rankin, Adam A., Vice-President, British Astronomical Association, West of 

Scotland Branch, 324 Crow Road, Broomhill, Glasgow, W. 

* Rankin e, John, K.C., M.A., LL.D., Professor of the Law of Scotland in the 

University of Edinburgh, 23 Ainslie Place, Edinburgh 
Ratcliffe, Joseph Riley, M.B., C.M., c/o The Librarian, The University, 
Birmingham 

Raw, Nathan, M.D. , M.R. C.P. (London), B.S., F. R.C.S., D.P.H., 66 Rodney 
Street, Liverpool 

Readman, J. B., D.Sc., F.C.S., Belmont, Hereford 480 

Redwood, Sir Boverton, Bt., D.Sc. (Hon.), F. I.C., F.C.S., A.Inst.C.E., The 
Cloisters, 18 Avenue Road, Regent’s Park, London, N.W. 

Rees-Roberts, John Vernon, M.D., D.Sc., D.P.H., Barrister-at-Law, National 
Liberal Club, Whitehall Place, London 

Reid, George Archdall O’Brien, M.B., C.M., 9 Victoria Road South, Southsea, 
Hants 

Reid, Harry Avery, F.R.C.V.S., D.V.H., Bacteriologist and Pathologist, .Depart- 
ment of Agriculture, Wellington, New Zealand 

* Rennie, John, D.Sc., Lecturer on Parasitology, and Assistant to the Professor of 

Natural History, University of Aberdeen, 60 Desswood Place, Aberdeen 485 
Renshaw, Graham, M.B., M.R.C.S., L.R.C.P., L.S.A., Surgeon, Bridge House, 
Sale, Manchester 

* Richardson, Harry, M.Inst.E.E., M.Inst.M.E., General Manager and Chief 

Engineer, Electricity Supply, Dundee and District, The Cottage, Craigie, 
Broughty Ferry 

Richardson, Linsdall, F.L.S., F.G.S., Organising Inspector of Technical Educa- 
tion for the Gloucestershire Education Committee, 10 Oxford Parade, 
Cheltenham 

Richardson, Ralph, W.S., 10 Magdala Place, Edinburgh 

* Ritchie, James Bonnyman, B.Sc., Science Master, Kelvinside Academy, Glasgow 490 

* Ritchie, William Thomas, M.D., F.R.C.P.E., 9 Atholl Place, Edinburgh 
Roberts, Alexander William, D.Sc., F.R.A.S., Lovedale, South Africa 
Roberts, D. Lloyd, M.D., F.R.C.P.L., 23 St John Street, Manchester 

* Robertson, Joseph M ‘Gregor, M.B., C.M., 26 Buckingham Terrace, Glasgow 

* Robertson, Robert, M.A., 25 Mansionhouse Road, Edinburgh 495 

* Robertson, Robert A., M.A. B.Sc., Lecturer on Botany in the University of St 

Andrews 



333 

Service on 
Council, etc. 



334 

Date of 
Election. 

1896 

1910 

1881 

1909 
1906 

1902 
1880 

1904 

1906 
1914 
1912 

1903 
1903 

1891 

1900 

1885 

1880 

1889 

1902 
1871 
1908 
1900 

1911 

1900 

1903 

1901 
1891 

1882 

1885 

1911 

1907 

1880 

1899 

1880 

1910 



Proceedings of the Eoyal Society of Edinburgh. 



c. 



0 . 

!. K. 



C. 



C. 

0 . 



C. 

C. 



!. K. 
C. 

C. 



* Robertson, W. G. Aitchison, D.Sc., M.D., F.R. C.P.E., 2 Mayfield Gardens, Edin- 

burgh 

* Robinson, Arthur, M.D., M.R.C.S., Professor of Anatomy, University of Edin-J 

burgh, 35 Coates Gardens, Edinburgh (Secretary) 1 

Rosebery, the Right Hon. the Earl of, K.G., K.T., LL.D., D.C.L. , F.R.S., 
Dalmeny Park, Edinburgh 

* Ross, Alex. David, M.A. , D.Sc., F. R.A. S., Professor of Mathematics and Physics, 

University of Western Australia, Perth, Western Australia 500 

* Russell, Alexander Durie, B.Sc., Mathematical Master, Falkirk High School, 

Dunaura, Heugh Street, Falkirk 

* Russell, James, 22 Glenorchy Terrace, Edinburgh 

Russell, Sir James A., M.A., B.Sc.,M.B., F.R.C.P.E., LL.D., Woodville, Canaan 
Lane, Edinburgh 

Sachs, Edwin O. , Architect, Chairman of the British Fire Prevention Committee, 
Vice-President of the International Fire Service Council, 8 Waterloo Place, 
Pall Mall, London, S.W. 

Saleeby, Caleb William, M.D., 13 Greville Place, London 505 

* Salvesen, Theodore Emile, 37 Inverleith Place, Edinburgh 

* Sampson, Ralph Allen, M.A., D.Sc., F.R.S., Astronomer Royal for Scotland, 

Professor of Astronomy, University, Edinburgh, Royal Observatory, Edinburgh 

* Samuel, John S. , 8 Park Avenue, Glasgow 

* Sarolea, Charles, Ph.D., D.Litt., Lecturer on French Language, Literature, and 

Romance Philology, University of Edinburgh, 21 Royal Terrace, Edinburgh 
Sawyer, Sir James, Kt., M.D., F.R.C.P., F.S.A., J.P., Consulting Physician to 
the Queen’s Hospital, 31 Temple Row, Birmingham 510 

* Schafer, Sir Edward Albert, M.R.C.S., LL.D., F.R.S. (Vice-President), I 

Professor of Physiology in the University of Edinburgh | 

Scott, Alexander, M.A., D.Sc., F.R.S., 34 Upper Hamilton Terrace, London, N.W. 
Scott, J. H., M.B., C.M., M.R.C.S., Professor of Anatomy in the University of 
Otago, New Zealand 

Scougal, A. E., M.A., LL.D., formerly H.M. Senior Chief Inspector of Schools 
and Inspector of Training Colleges, 1 Wester Coates Avenue, Edinburgh 
Senn, Nicholas, M.D., LL.D., Professor of Surgery, Rush Medical College, 
Chicago , U. S. A . 515 

Simpson, Sir A. R., M.D., Emeritus Professor of Midwifery in the University of 
Edinburgh. 52 Queen Street, Edinburgh 

* Simpson, George Freeland Barbour, M.D., F.R.C.P.E., F.R.C.S.E., 43 Manor 

Place, Edinburgh 

* Simpson, James Young, M.A. , D.Sc., Professor of Natural Science in the New 

College, Edinburgh, 25 Chester Street, Edinburgh 
Simpson, Sutherland, M.D., D.Sc. (Edin.), Professor of Physiology, Medical 
College, Cornell University, Ithaca, N.Y., U.S.A., 118 Eddy Street, Ithaca, 
N.Y., U.S.A. 

Sinhjee, Sir Bhagvat, G.C.I.E., M.D., LL.D. Edin., H. H. the Thakur Sahib 
of Gondal, Gondal, Kathiawar, Bombay, India 520 

* Skinner, Robert Taylor, M.A., Governor and Head Master, Donaldson’s Hospital, 

Edinburgh 

* Smart, Edward, B.A., B.Sc., Tillyloss, Tullylumb Terrace, Perth 

* Smith, Alexander, B.Sc., Ph.D., Department of Chemistry, Columbia University, 

New York, N.Y., U.S.A. 

Smith, C. Michie, C. I.E., B.Sc., F.R.A.S. , formerly Director of the Kodaikanal and 
Madras Observatories, Winsford, Kodaikanal, South India 
Smith, George, F.C.S., 5 Rosehall Terrace, Falkirk 525 

* Smith, Stephen, B.Sc., Goldsmith, 31 Grange Loan, Edinburgh 

Smith, William Ramsay, D.Sc., M.D., C.M., Permanent Head of the Health 
Department, South Australia, Belair, South Australia 
Smith, William Robert, M.D., D.Sc., LL.D., Professor of Forensic Medicine and 
Toxicology in King’s College, University of London, and Principal of the 
Royal Institute of Public Health, 36 Russell Square, London, W.C. 

Snell, ErnestHugh, M.D., B.Sc., D.P.H. Camb., Medical Officer of Health, Coventry 
Sollas, W. J., M. A., D.Sc., LL.D., F.R.S., Fellow of University College, Oxford, 
and Professor of Geology and Palaeontology in the University of Oxford 530 

* Somerville, Robert, B.Sc., Science Master, High School, Dunfermline, 31 Cameron 

Street, Dunfermline 



Service on 
Council, etc. 



1910-1912. 

Sec. 

1912- 



1912- 



1900-03, 

1906-09. 

V.P. 

1913- 



Date of 

Election. 

1889 

1911 

1882 

1896 

1874 

1906 

1891 

1914 

1912 

1910 

1886 

1884 

1888 

1902 

1889 

1906 

1907 

1903 

1905 

1912 

1885 

1904 

1898 

1895 

1890 

1870 

1899 

1892 

1885 

1907 

1905 

1887 

1911 

1896 

1903 

1906 

1887 

1906 

1880 

1899 

1912 



Alphabetical List of the Ordinary Fellows of the Society. 



Somerville, AVm. , M.A. , D.Sc., D. Oec., Sibthorpian Professor of Rural Economy 
and Fellow of St John’s College in the University of Oxford, 121 Banbury 
Road, Oxford 

* Sommerville, Duncan M‘Laren Young, M.A., D.Sc., Professor of Pure and 

Applied Mathematics, Victoria College, Wellington, New Zealand 
Sorley, James, 82 Onslow Gardens, London 

* Spence, Frank, M.A., B.Sc., 25 Craiglea Drive, Edinburgh 535 

Sprague, T. B., M.A., LL.D., Actuary, 29 Buckingham Terrace, Edinburgh 
Squance, Thomas Coke, M.D., F.R.M.S., F.S.A.Scot., Physician and Pathologist 

in the Sunderland Infirmary, President Sunderland Antiquarian Society, 
Sunderland Naturalists’ Association, 15 Grange Crescent, Sunderland 

* Stanfield, Richard, Professor of Mechanics and Engineering in the Heriot-Watt 

College, Edinburgh 

* Steggall, John Edward Aloysius, M.A. , Professor of Mathematics at University 

College, Dundee, in St Andrews University, Woodend, Perth Road, Dundee 
Stephenson, John, M. B., D.Sc. (Lond.), Indian Medical Service, Professor of 
Biology, Government College, Lahore, India. 540 

* Stephenson, Thomas, F.C.S., Editor of the Presenter, Examiner to the Pharma- 

ceutical Society, 9 Woodburn Terrace, Edinburgh 
Stevenson, Charles A., B.Sc., M.Inst.C.E., 28 Douglas Crescent, Edinburgh 
Stevenson, David Alan, B.Sc., M.Inst.C.E., 84 George Street, Edinburgh 
Stewart, Charles Hunter, D.Sc., M.B., C.M., Professor of Public Health in the 
University of Edinburgh, Usher Institute of Public Health, Warrender 
Park Road, Edinburgh 

* Stockdale, Herbert Fitton, Director of the Royal Technical College, Glasgow, 

Clairinch, Upper Helensburgh, Dumbartonshire 545 

Stockman, Ralph, M.D., F.R.C.P.E., Professor of Materia Medica and Therapeutics 
in the University of Glasgow 

Story, Fraser, Professor of Forestry, University College, Bangor, North Wales 

* Strong, John, M.A., Rector of Montrose Academy, Peel Place, Montrose 
Sutherland, David W. , M.D., M.R.C.P. , Captain, Indian Medical Service, 

Professor of Pathology and Materia Medica, Medical College, Lahore, India 
Swithinbank, Harold William, Denham Court, Denham, Bucks 550 

* Syme, William Smith, M.D. (Edin. ), 10 India Street, Glasgow 

Symington, Johnson, M.D., F.R.C.S.E., F.R.S., Professor of Anatomy in Queen’s 
College, Belfast 

* Tait, John W., B.Sc., Rector of Leith Academy, 18 Netherby Road, Leith 
Tait, William Archer, D.Sc., M.Inst.C.E., 38 George Square, Edinburgh 
Talmage, James Edward, D.Sc., Ph.D., F.R.M.S., F.G.S., Professor of Geology, 

University of Utah, Salt Lake City, Utah, U.S.A. 555 

Tanakadate, Aikitu, Professor of Natural Philosophy in the Imperial University 
of Japan, Tokyo, Japan 

Tatlock, Robert R., F.C.S. , City Analyst’s Office, 156 Bath Street, Glasgow 

* Taylor, James, M. A. , Mathematical Master in the Edinburgh Academy 
Thackwell, J. B. , M.B., C.M., 423 a Battersea Park Road, London, S. W. 

Thompson, D’Arcy W. , C.B., B.A. , F. L.S., Professor of Natural History in) 
University College, Dundee 560 j 

* Thompson, John Hannay, M.Sc. (Durh.), M.Inst.C.E., M. Inst.Mech.E., Engineer 

to the Dundee Harbour Trust, Sorbie, 10 Balgillo Terrace, Brough ty Ferry 

* Thoms, Alexander, 7 Playfair Terrace, St Andrews 

Thomson, Andrew, M.A., D.Sc., F.I.C., Rector, Perth Academy, Ardenlea, 
Pitcullen, Perth 

* Thomson, Frank Wyville, M.A., M.B., C.M., D.P.H., D.T.M., Lt.-Col. I.M.S. 

(Retired), Bonsyde, Linlithgow 

* Thomson, George Ritchie, M.B., C.M., General Hospital, Johannesburg, Transvaal 565 
Thomson, George S., F.C.S. , Ferma Albion, Marculesci, Roumania 

* Thomson, Gilbert, M.Inst.C.E., 164 Bath Street, Glasgow 

Thomson, J. Arthur, M.A., LL.D., Regius Professor of Natural History in the 
University of Aberdeen 

Thomson, James Stuart, F.L.S. , Zoological Department, University, Manchester 
Thomson, John Millar, LL.D., F.R.S., Professor of Chemistry in King’s College, 
London, 18 Lansdowne Road, London, W. 570 

* Thomson, R. Tatlock, F.C.S., 156 Bath Street, Glasgow 

Thomson, Robert Black, M.B., Edin., Professor of Anatomy, South African 
College, Cape Town 



335 



Service on 
Council, etc. 



1885-87. 



1903-05. 

1892- 

1914- 

1892-95, 

1896-99, 

1907-10, 

1912- 



1906-08. 



336 

Date of 

Election. 

1870 

1882 

1876 

1911 

1914 

1888 

1905 

1906 

1861 

1895 

1898 

1889 

1910 

1911 

1891 

1873 

1902 

1886 

1898 

1891 

1907 

1901 

1911 

1900 

1910 

1907 

1911 

1911 

1896 

1907 

1903 

1904 

1896 

1909 

1896 



Proceedings of the Royal Society of Edinburgh. 



Service on 
Council, etc. 



Thomson, Spencer C., Actuary, 10 Eglinton Crescent, Edinburgh 
Thomson, Wm., M.A., B.Sc., LL.D., Registrar, University of the Cape of Good 
Hope. University Buildings, Cape Town 

Thomson, William, Royal Institution, Manchester 575 

* Tosh, James Ramsay, M.A., D.Sc. (St Ands.), Thursday Island, Queensland, 

Australia 

Tredgold, Alfred Frank, L.R.C.P., M.R.C.S., Hon. Consulting Physician to National 
Association for the Feeble-minded, 6 Dapdune Crescent, Guildford, Surrey 
Turnbull, Andrew H., Actuary, The Elms, Whitehouse Loan, Edinburgh 

* Turner, Arthur Logan, M.D., F.R.C.S.E., 27 Walker Street, Edinburgh 

* Turner, Dawson F. D., B.A., M.D., F.R.C.P.E., M.R.C.P., Lecturer on Medical 

Physics, Surgeons’ Hall, Physician in charge of Radium Treatment, Royal 
Infirmary, Edinburgh, 37 George Square, Edinburgh 580 r 



Turner, Sir William, K.C.B., M.B., F.R.C.S.L. and E., LL.D., D.C.L., D.Sc., 
F.R.S. , Late Pres. R.S.E., Knight of the Royal Prussian Order Pour le , 
Merite, Principal and Vice-Chancellor of the University of Edinburgh, 
6 Eton Terrace, Edinburgh 



Turton. Albert H., M. I.M.M., 171 George Road, Erdington, Birmingham 

* Tweedie, Charles, M.A. , B.Sc., Lecturer on Mathematics in the University of 

Edinburgh, Duns, Berwickshire 

Underhill, T. Edgar, M.D., F.R.C.S.E., Dunedin, Barnt Green, Worcestershire 
Vincent, Swale, M.D. Lond., D.Sc. Edin., etc., Professor of Physiology, University 
of Manitoba, Winnipeg, Canada 585 

* Walker, Henry, M.A. , D.Sc., Head Physics Master, Kilmarnock Academy and 

Technical School, 30 M‘Lelland Drive, Kilmarnock 

* Walker, James, D.Sc., Ph.D., LL.D., F.R.S., Professor of Chemistry in the 

University of Edinburgh, 5 Wester Coates Road, Edinburgh 
Walker, Robert, M.A., LL.D., University, Aberdeen 

* Wallace, Alexander G., M.A., 56 Fonthill Road, Aberdeen 

Wallace, R., F.L.S. , Professor of Agriculture and Rural Economy in the University 
of Edinburgh 590 

Wallace, Wm., M.A., Belvedere, Alberta, Canada 

* Walmsley, R. Mullineux, D.Sc., Principal of the Northampton Institute, Clerken- 

well, London 

Waters, E. Wynston, Medical Officer, H.B.M. Administration, E. Africa, Malindi, 
British East Africa Protectorate, via Mombasa 

* Waterston, David, M.A., M.D., F. R.C.S.E. , Professor of Anatomy, University, 

St Andrews 

* Watson, James A. S., B.Sc., etc., Assistant in Agriculture, University of Edin- 

burgh, 15 Dick Place, Edinburgh 595 

* Watson, Thomas P., M.A., B.Sc., Principal, Keighley Institute, Keighley 

* Watson, William John, M.A., LL.D. Aberdeen, B.A. Oxon., Professor of Celtic 

Languages and Literature, University, Edinburgh, 17 Merchiston Avenue, 
Edinburgh 

* Watt, Andrew, M. A., Secretary to the Scottish Meteorological Society, 6 Woodburn 

Terrace, Edinburgh 

Watt, James, W.S., F. F.A., 24 Rothesay Terrace, Edinburgh 

* Watt, Rev. Lauclilan Maclean, B.D., Minister of St Stephen’s Parish, 7 Royal 

Circus, Edinburgh 600 

Webster, John Clarence, B.A., M.D., F.R.C.P.E., Professorof Obstetrics and Gynae- 
cology, Rush Medical College, 1748 Harrison Street, Chicago, 111., U.S.A. 

* Wedderburn, Ernest Maclagan, M.A., LL.B., W.S. , D.Sc., 7 Dean Park Crescent, 

Edinburgh 

* Wedderburn, J. H. Maclagan, M.A. , D.Sc., 95MercerStreet, Princeton, N.J., U.S.A. 
Wedderspoon, William Gibson, M.A., LL.D., Indian Educational Service, Senior 

Inspector of Schools, Burma, The Education Office, Rangoon, Burma 
Wenley, Robert Mark, M.A., D.Sc., D.Phil. , Litt.D., LL.D., D. C.L., Professor 
of Philosophy in the University of Michigan, Ann Arbor, U.S.A. 605 

* Westergaard, Reginald Ludovic Andreas Emil, Ph.D., Professor of Technical 

Mycology, Heriot- Watt College, Hafnia, Liberton, Edinburgh 
White, Philip J., M.B., Professor of Zoology in University College, Bangor, North 
Wales 



1866-68, 

1895-97. 

1913- 

Sec. 

1869-91. 

V-P 

1891-95, 

1897-1903. 

P. 

1908-1913. 

1907-10. 



1903-05, 

1910-13. 



1912-14. 



1913- 



List of Honorary Fellows, etc. 



337 



Date of 
Election. 

1911 

1912 
1879 
1908 

1910 C. 
1900 

1911 
1902 

1895 

1882 

1891 

1902 

1908 

1886 C. 

1884 

1911 

1890 

1896 

1882 



1892 



1896 

1904 



C. 



* Whittaker, Charles Richard, F. R.C.S, (Edin.), F.S.A. (Scot. ), Lynwood, Hatton 

Place, Edinburgh 

* Whittaker, Edmund Taylor, Sc.D., F.R.S., Professor of Mathematics in the 

University of Edinburgh, 35 George Square, Edinburgh 
Will, John Charles Ogil vie, of Newton of Pitfodels, M.D. , 17 Bon- Accord Square, 
Aberdeen 610 

* Williamson, Henry Charles, M.A., D.Sc. , Naturalist to the Fishery Board for 

Scotland, Marine Laboratory, Aberdeen 

* Williamson, William, 9 Plewlands Terrace, Edinburgh 
Wilson, Alfred C. , F.C.S., Yoewood Croft, Stockton-on-Tees 

* Wilson, Andrew, M.Inst. C.E., 51 Queen Street, Edinburgh 

* Wilson, Charles T. R., M.A., F.R.S., 21 Grange Road, Cambridge, Sidney 

Sussex College, Cambridge 615 

Wilson -Barker, David, R.N.R., F. R.G.S., Captain-Superintendent Thames Nautical 
Training College, H.M.S. “Worcester,” off Greenhithe, Kent 
Wilson, George, M.A. , M.D., LL.D. 

* Wilson, John Hardie, D.Sc., University of St Andrews, 39 South Street, St 

Andrews 

Wilson, William Wright, F.R.C.S.E., M.R.C.S., Cottesbrook House, Acock’s 
Green, Birmingham 

* Wood, Thomas, M.D. , Eastwood, 182 Ferry Road, Bonnington, Leith 620 

Woodhead, German Sims, M.D. , F.R.C.P.E., Professor of Pathology in the 

University of Cambridge 

Woods, G. A., M.R.C.S., 1 Hammelton Road, Bromley, Kent 

* Wrigley, Ruric Whitehead, B.A. (Cantab.), Assistant Astronomer, Royal Observa- 

tory, Edinburgh 

Wright, Johnstone Christie, Conservative Club, Edinburgh 

* Wright, Sir Robert Patrick, Chairman of the Board of Agriculture for Scotland, 

Kingarth, Colinton, Midlothian 625 

Young, Frank W., F.C.S., H.M. Inspector of Science and Art Schools, 
32 Buckingham Terrace, Botanic Gardens, Glasgow 
Young, George, Ph.D., “ Bradda,” Church Crescent, Church End, Finchley, 
London, N. 

* Young, James Buchanan, M.B., D.Sc., Dalveen, Braeside, Liberton 

Young, R. B., M.A., D.Sc., F.G.S., Professor of Geology and Mineralogy 
in the South African School of Mines and Technology, Johannesburg, 
Transvaal 



Service on 
Council, etc. 



1912- 



1887-90. 






LIST OF HONORARY FELLOWS OF THE SOCIETY 

At January 1, 1914. 

HIS MOST GRACIOUS MAJESTY THE KING. 



Foreigners (limited to thirty-six by Law X). 

Elected, 

1897 Emile Hilaire Amagat, Membre de l’lnstitut, St Satur, Cher, France. 

1900 Arthur Auwers, Belle vue-Strasse 55, Berlin-Lichterfelde, Germany. 

1900 Adolf Ritter von Baeyer, Universitat, Miinchen, Germany. 

1905 Waldemar Christofer Brogger, K. Frederiks Universitet, Christiania, Norway. 

1905 Moritz Cantor, Gaisbergstrasse 15, Heidelberg, Germany. 

1902 Jean Gaston Darboux, Secretariat de l’lnstitut, Paris, France. 

1910 Hugo de Vries, Universiteit, Amsterdam, Holland. 

1905 Paul Ehrlich, K. Institut fur Experimentelle Therapie, Sandhofstrasse 44, Frankfurt-a.-M., 
Germany. 

1908 Emil Fischer, Universitat, Berlin, Germany. 

1910 Karl F. von Goebel, Universitat, Miinchen, Germany. 

1905 Paul Heinrich von Groth, Universitat, Munchen, Germany. 

1888 Ernst Haeckel, Universitat, Jena, Germany. 

1913 George Ellery Hale, Mount Wilson Solar Observatory (Carnegie Institution of Washington), 
Pasadena, California, U.S.A. 

1883 Julius Hann, Universitat, Wien, Austria. 

1913 Emil Clement Jungfleisch, College de France, Paris, France. 

1910 Jacobus Cornelius Kapteyn, Universiteit, Groningen, Holland. 

vol. xxxiv. 22 



338 



Proceedings of the Royal Society of Edinburgh. 

Elected 

1897 Gabriel Lippmann, Universite, Paris, France. 

1895 Carl Menger, Wienix., Fuchstallerg, 2, Austria. 

1910 Elie Metchnikoff, Institut Pasteur, Paris, France. 

1910 Albert Abraham Michelson, University, Chicago, U.S.A. 

1897 Fridtjof Nansen, K. Frederiks Universitet, Christiania, Norway. 

1908 Henry Fairfield Osborn, Columbia University and American Museum of Natural History, 
New York, N.Y., U.S.A. 

1910 Wilhelm Ostwald, Gross-Bothen, bei Leipzig, Germany. 

1908 Ivan Petrovitch Pawlov, Wedenskaja Strasse 4, St Petersburg, Russia. 

1910 Frederick Ward Putnam, Peabody Museum of Harvard University, Cambridge, Mass. , 

1889 Georg Hermann Quincke, Bergstrasse 41, Heidelberg, Germany. 

1913 Santiago Ramon y Cajal, Universidad, Madrid, Spain. 

1908 Magnus Gustaf Retzius, Hogskolan, Stockholm, Sweden. 

1908 Augusto Righi, Regia Universita, Bologna, Italy. 

1913 Yito Volterra, Regia Universita, Rome, Italy. 

1905 Wilhelm Waldeyer, Universitat, Berlin, Germany. 

1905 Wilhelm Wundt, Universitat, Leipzig, Germany. 

1913 Charles Rene Zeiller, Ecole Nationale Superieure des Mines, Paris, France. 

Total, 33. 

British Subjects (limited to twenty by Law X). 

1900 Sir David Ferrier, Kt., M.A., M.D., LL.D., F.R.S., Emer. Professor of Neuro-Pathology, 
King’s College, London, 34 Cavendish Square, London, W. 

1900 Andrew Russell Forsyth, M.A. , Sc.D., LL.D., Math.D. , F.R.S., Chief Professor of 
Mathematics in the Imperial College of Science and Technology, London, formerly 
Sadlerian Professor of Pure Mathematics in the University of Cambridge, Imperial 
College of Science, London, S.W. 

1910 Sir James George Frazer, D.C.L. , LL.D., Litt.D., F.B.A. , Fellow of Trinity College, Cam- 
bridge, Professor of Social Anthropology in the University of Liverpool, Trinity College, 
Cambridge. 

1908 Sir Alexander B. W. Kennedy, Kt., LL.D., F.R.S., Past Pres. Inst. C.E. , 1 Queen Anne 
Street, Cavendish Square, London, W. 

1913 Horace Lamb, M.A., Sc.D., D.Sc., LL.D., F. R.S. , Professor of Mathematics in the 
University of Manchester. 

1908 Sir Edwin Ray Lankester, K.C.B., LL.D., F.R.S. , 29 Thurloe Place, S. Kensington, 
London, S.W. 

1910 Sir Joseph Larmor, Kt., M.A., D.Sc., LL.D., D.C.L. , F.R.S. , M. P. University of Cambridge 
since 1911, Lucasian Professor of Mathematics in the University of Cambridge, St John’s 
College, Cambridge. 

1900 Archibald Liversidge, M.A., LL.D., F.R.S., Em.-Professor of Chemistry in the University of 
Sydney, Fieldhead, Combe Warren, Kingston, Surrey. 

1908 Sir James A. H. Murray, LL.D., D.C.L., D.Litt., Ph.D., Litt.D., F.S.A., Corresp. Member 
of the Institute of France, etc., Editor of the Oxford English Dictionary, Oxford. 

1905 Sir William Ramsay, K.C.B*, LL.D., F.R.S., formerly Professor of Chemistry in the 
University College, London, 19 Chester Terrace, Regent’s Park, London, N.W. 

1886 The Rt. Hon. Lord Rayleigh, O. M., P.C. , J.P. , D.C.L., LL.D., D.Sc. Dub., F.R.S., Corresp. 
Mem. Inst, of France, Terling Place, Witham, Essex. 

1908 Charles Scott Sherrington, M.A., M.D., LL.D., F.R.S., Waynflete Professor of Physiology in 

the University of Oxford, Physiological Laboratory, Oxford. 

1913 Sir William Turner Thiselton-Dyer, K.C.M.G., C.I.E., M.A., LL.D., F.R.S., formerly 
Director of the Royal Botanic Gardens, Kew ; The Ferns, Witcombe, Gloucester. 

1905 Sir Joseph John Thomson, D.Sc., LL.D., F.R.S., Cavendish Professor of Experimental 
Physics, University of Cambridge, Trinity College, Cambridge. 

1909 Sir Thomas Edward Thorpe, Kt. , C.B. , D.Sc., LL.D., F.R.S., formerly Principal of the 

Government Laboratories, Imperial College of Science and Technology, South Kensington, 
London, S.W., Wliinfield Salcombe, South Devon. 

Total, 15. 



Ordinary Fellows of the Society Elected. 



339 



ORDINARY FELLOWS OF THE SOCIETY ELECTED 

During Sessio7i 1913 - 14 . 

(Arranged according to their date of election.) 

17 th November 1913. 

Edward Philip Harrison, Ph.D. 

1st December 1913. 

William Barron Coutts, M.A., B.Sc. John Edward Gemmell, M.B., C.M. (Edin.). 

William Fraser. Alfred Oswald. 

John William Pare, M.B., C.M. (Edin.), M.D., L.D.S. (Eng.). 

19 th January 1914. 

Spencer Mort, M.D., Ch.B., F.R.C.S.E. Joseph Pearson, D.Sc., F.L.S, 

16th February 1914. 

Robert John Harvey-Gibson, M.A., F.L.S. , D.L. for the 
County Palatine of Lancaster, M.R.S.G.S. 

John Noble Jack. 

25 th May 1914. 

Alexander Charles Cumming, D.Sc. Graham Renshaw, M.B., M.R.C.S., L.R.C.P., 

Basil Alexander Pilkington. L.S.A. 

Peter Ramsay, M.A., B.S.C. James Bonnyman Ritchie, B.Sc. 

Theodore Emile Salvesen. 

15th June 1914. 

Alexander Gibb, A.M.Inst.C.E. 

6th July 1914. 

Francis John Lewis, D.Sc., F.L.S. 

Archibald M‘Kendrick, F.R.C.S.E., D.P.H., L.D.S. 

Alfred Frank Tredgold, L.R.C.P., M.R.C.S. 



ORDINARY FELLOWS DECEASED AND RESIGNED 

During Session 1913 - 14 . 

DECEASED. 

James A. Macdonald, M.A., B.Sc. 

John Sturgeon Mackay, M.A., LL.D. 

Sir John Murray, K.C.B., LL.D., Ph.D., 
D.Sc., F.R.S. 

R. Traill Omond. 

RESIGNED. 

Rev. John H. Burn. Charles B. Boog Watson. 



John Gibson, Ph.D. 

J. W. Inglis, M.Inst.C.E. 

Lieut. George J ohnstone, R. N. R. 
John Macallan, F.I.C. 



FOREIGN HONORARY FELLOW DECEASED. 

Eduard Suess. 



BRITISH HONORARY 

Sir Robert Stawell Ball, Kt., LL.D., F.R.S., 
M.RJ.A. 

Coh Alexander Ross Clarke, C.B. , R.E., 
F R S 

Sir David Gill, K.C.B., LL.D., F.R.S. 



FELLOWS DECEASED. 

Albert C. L. G. Gunther, Ph.D., F.R.S. 
George William Hill. 

Alfred Russel Wallace, O.M., LL.D., 
D.C.L., F.R.S. 



340 Proceedings of the Royal Society of Edinburgh. [Sess. 



List of Library Exchanges, Presentations, etc. 

1. Transactions and Proceedings of Learned Societies, Academies, 

ETC., RECEIVED BY EXCHANGE OF PUBLICATIONS, AND LlST OF 

Public Institutions entitled to receive Copies of the 
Transactions and Proceedings of the Royal Society of 
Edinburgh. {For convenience certain Presentations are included 
in this List.) 

T.P. prefixed to a name indicates that the Institution is entitled to receive Transactions and 
Proceedings . P. indicates Proceedings . 

AFRICA (BRITISH CENTRAL). 

Zomba. — Scientific Department. Meteorological Observations, Fol. {Presented 
by H.M. Acting Commissioner and Consul-General .) 

AMERICA (NORTH). {See CANADA, UNITED STATES, and MEXICO.) 

AMERICA (SOUTH). 

t.p. Buenos Ayres (Argentine Republic). — Museo Nacional. Anales. 
p. Sociedad Physis. Boletin. 

Oficina Meteorologica Argentina. Anales. ( Presented .) 

Cordoba — 

t.p. Academia Nacional de Ciencias de la Republica Argentina. Boletin. 

t.p. National Observatory. Annals. — Maps. 

t.p. La Plata (Argentine Republic). — Museo de La Plata. 

Lima (Peru). Cuerpo de Ingenieros de Minas del Peru. Boletin. ( Presented .) 
p. Montevideo (Uruguay). — Museo Nacional. Anales (Flora Uruguay). 

t.p. Para (Brazil). — Museu Paraense de Historia Natural e Ethnographia. Boletin. 
p. Quito (Ecuador). — Observatorio Astronomico y Meteor ologico. 

Rio de Janeiro (Brazil) — 
t.p. Observatorio. Annuario. — Boletin Mensal. 

p. Museu Nacional. Revista (Archivos). 

Santiago (Chili) — 

t.p. Societe Scientifique du Chili. Actes. 

p. Deutscher Wissenschaftlicher Verein. 

p. San Salvador. — Observatorio Astronomico y Meteor ologico. 

Valparaiso (Chili). — Servicio Meteor ologico. Annuario. {Presented.) 



AUSTRALIA. 

Australasian Association for the Advancement of Science. — Reports. {Pre- 
sented.) 



341 



1913-14.] List of Library Exchanges, Presentations, etc. 

Adelaide — 

p. University Library. 

p. Royal Society of South Australia. Transactions and Proceedings. — Memoirs, 
p. Royal Geographical Society of Australasia ( South Australian Branch). 
Proceedings. 

Observatory. Meteorological Observations. 4 to. ( Presented .) 

Brisbane — 

t.p. University of Queensland. 

p. Royal Society of Queensland. Transactions. 

p. Royal Geographical Society ( Queensland Branch). Queensland Geographical 
J ournal. 

p. Government Meteorological Office. 

p. Water Supply Department. 

p. Geelong (Yictoria). — Gordon Technical College. 
t.p. Hobart. — Royal Society of Tasmania. Proceedings. 

Melbourne — 

Commonwealth Bureau of Census and Statistics. Official Year Book. 

By G. H. Knibbs. ( Presented .) 

National Museum. Memoirs. ( Presented .) 

t.p. University Library. 

p. Royal Society of Victoria. Proceedings. — Transactions. 

Perth, W.A. — 

p. Geological Survey. Annual Progress Reports. — Bulletins. 

Government Statistician’s Office. Monthly Statistical Abstract. ( Presented .) 
Sydney — 

t.p. University Library. Calendar. — Reprints of Papers from Science Laboratories. 
t.p. Department of Mines and Agriculture ( Geological Survey ), N.S.W. 

Records. — Annual Reports. — Palaeontology. Mineral Resources. 
t.p. Linnean Society of New South Wales. Proceedings. 
t.p. Royal Society of New South Wales. Journal and Proceedings, 
p. Australian Museum. Records. — Reports. — Memoirs. — Catalogues. 

N.S.W. Government. Fisheries Report. ( Presented .) 



AUSTRIA. 

Cracow — 

t.p. Academie des Sciences. Rozprawy Wydzialu matematyczno-przyrodniezego 
(Proceedings, Math, and Nat. Sciences Cl.). — Rozprawy Wydzialu 
filologicznego (Proc., Philological Section). — Rozprawy Wydzialu his- 
toryczno-filozoficznego (Proc., Hist.-Phil. Section). — Sprawozdanie Komisyi 
do badania historyi sztuki w Polsce (Proc., Commission on History of Art 
in Poland). — Sprawozdanie Komisyi fizyjograficznej (Proc., Commission 
on Physiography). — Geological Atlas of Galicia; Text, Maps. — Bulletin 
International, etc. 

Gratz — 

t.p. Naturwissenschaftlicher Verein fur Steiermark. Mittheilungen. 
p. Chemisches Institut der K. K. Universitat. 
p. Lemberg. — Societe Scientifique de Chevtchenko . 



342 



p. 

T.P. 

T.P. 

T.P. 

P. 

P. 

P. 

P. 

T.P. 

T.P. 

T.P. 

T.P. 

P. 



T.P. 

T.P. 

T.P. 

T.P. 



Proceedings of the Royal Society of Edinburgh. [Sess. 

Prague — 

Deutscher Nat. -Med. Vereinfilr Bohmen “Lotos.” — “Lotos.” 

K. K. Stermvarte. Magnetische und Meteorologische Beobachtungen. 
Astronomische Beobachtungen. 

K. Bohmische Gesellschaft. Sitzungsberichte : Math.-Naturw. Classe; Phil - 
Hist.-Philol. Classe.— Jahresbericht, — and other publications. 

Ceshd Akademie Cisare Frantiska Josef a pro Vedy Slovesnost a Umeni. 
Almanach. — Yestnik (Proceedings). — Rozpravy (Transactions) : Phil.- 
Hist. Class ; Math.-Phys. Cl. ; Philol. Cl. — Historicky Archiv. — Bulletin 
International, Resume des Travaux presentes, — and other publications of 
the Academy. 

Sarajevo (Bosnia). — The Governor-General of Bosnia-Herzegovina. Ergebnisse 
der Meteorologischen Beobachtungen. 

Trieste — 

Societa Adriatica di Scienze Naturali. 

Museo Civico di Storia Natnrale. 

Osservatorio Marittimo. Rapporto Annuale. 

Vienna — 

Kais. Akademie der^ Wissenschaften. Denkschriften : Math.-Raturwissen- 
schaftliche Classe ; Philosophisch-Historische Classe — Sitzungsberichte 
der Math.-Raturwissenschaftlichen Classe; Abtheil. I., II.a, II.b, III.; 
Philosoph.-Historische Classe. — Almanach. — Mittheilungen der Erdbeben 
Commission. 

K. K. Geologische Reichsanstalt. Abhandlungen. — Jahrbiicher. — Verhand- 
lungen. 

Oesterreiclnsche Gesellschaft fur Meteorologie. Meteorologische Zeitschrift. 

K. K. Zoologisch - Botanische Gesellschaft. Verhandlungen. — Abhand- 
lungen. 

K. K. N aturhistorisches Hofmuseum. Annalen. 

K. K. Central- Anstalt fur Meteorologie und Erdmagnetismns. Jahrbiicher. 

4to. — Allgemeiner Bericht und Chronik. 8vo. (Presented.) 

K. K. Militar Geographisclies Institut. Astronomisch-Geodatischen Arbeiten. 
— Astronomische Arbeiten. 4to. — TAngenbestimmungen. 4to. — Die 

Ergebnisse der Triangulierungen. 4to. ( Presented .) 

Zoologisches Institut der Universitdt und der Zoologisch en Station in Triest. 
Arbeiten . ( Purchased,. ) 



BELGIUM. 



Brussels — 

Acadernie Roy ale des Sciences , des Lettres et des Beaux Arts de Belgique. 

Memoires. — Bulletins. — Annuaire. — Biographie Rationale. 

Musee Royal JHistoire Naturelle. Memoires. 

Musee du Congo. Annales. — Botanique. Zoologie. Ethnographie et. 
Antliropologie. Linguistique , etc. 

V Ohservatoire Royal de Belgique , Uccle. Annuaire. — Annales Astronomiques 
— Annales Meteorologiques.— Annales. — Physique du Globe. — Bulletin 
Climatologique.— Observations Meteorologiques. 



1913-14.] List of Library Exchanges, Presentations, etc. 



343 



T.P. 

P. 

T.P. 

T.P. 



P. 



P. 

T.P. 

P. 

P. 

T.P. 

T.P. 

P. 

T.P. 

T.P. 



T.P. 

P. 



T.P. 



Brussels — continued — 

Societe Scientifique. Annales. 

Societe Beige d’ Astronomie. Ciel et Terre. ( Purchased .) 

Ghent. — University Library. 

Louvain. — University Library. 

BOSNIA-HERZEGOYINA. (Bee AUSTRIA.) 

BULGARIA. 

Sofia. — Station Gentrale Meteorologique de Bulgarie. Bulletin Mensuel. — * 
Bulletins Annuaires. 



CANADA. 

Edmonton (Alberta). — Department of Agriculture. Annual Report. — 
(Presented.) 

Halifax (Nova Scotia). — Nova Scotian Institute of Science. Proceedings 
and Transactions. 

Kingston. — Queen’s University. 

Montreal — 

Natural History Society. Proceedings. 

Canadian Society of Civil Engineers. Transactions. — Annual Reports. 
Ottawa — 

Royal Society of Canada. Proceedings and Transactions. 

Geological Survey of Canada. Annual Reports. — Palaeozoic Fossils. — Maps, 
Memoirs, and other Publications. 

Literary and Scientific Society. Transactions. 

Quebec. — Literary and Philosophical Society. Transactions. 

Toronto — 

University. University Studies. (History. Psychological Series. Geological 
Series. Economic Series. Physiological Series. Biological Series. 
Physical Science Series. Papers from the Chemical Laboratory.) etc. 
Canadian Institute. Transactions. 

Royal Astronomical Society of Canada. Journal. — Astronomical Handbook. 



CAPE COLONY. (See UNION OF SOUTH AFRICA.) 



Colombo — 
Museum. 



CEYLON. 

Spolia Zeylanica. Annual Report. 



Hong Kong — 

Royal Observatory. 



CHINA. 

Monthly Meteorological Bulletin. — Report. 



344 



Proceedings of the Royal Society of Edinburgh. [Sess. 



DENMARK. 

Copenhagen— 

t.p. Academie Royale de Copenhague. Memoires : Classe des Sciences. — Oversigt. 
p. Naturhistorisk F overling. Videnskabelige Meddelelser. 

p. Danish Biological Station. Report. 

Conseil Permanent International pour V Exploration de la Mer. Publications 
de circonstance. — Rapports et Proces-Verbaux de Reunions. — Bulletin des 
Resultats acquis pendant les croisieres periodiques. — Bulletin Statistique. 
( Presented .) 

Kommissionen for Havundersogelser. Meddelelser : Serie Fiskeri. Serie 
Plankton. Serie Hydrografi. — Skrifter. ( Presented .) 

University (. Zoological Museum). Reports of the Danish Ingolf-Expedition. 
(Presented.) 



EGYPT. 

t.p. Cairo. — School of Medicine. Records. 

Ministry of Finance" (Survey Dept. : Archaeological Survey of Nubia). 
Bulletin, Reports, Papers. (Presented.) 



ENGLAND AND WALES. 

Birmingham — 

p. Philosophical Society. Proceedings. 

University. Calendar. (Presented.) 

Cambridge — 

t.p. Philosophical Society. Transactions and Proceedings. 

t.p. University Library. — Observatory. Report. — Observations. 

t.p. Cardiff. — University College of South Wales. 

Coventry. — Annual Report of the Health of the City. (Presented by Dr Snell.) 
p. Essex. — Essex Field Club. The Essex Naturalist. 

t.p. Greenwich. — Royal Observatory. Astronomical, Magnetical, and Meteorological 
Observations. — Photo-heliographic Results and other Publications. 
t.p. Harpenden (Herts.). — Rothamstead Exp. Station. (Lawes Agricultural Trust.) 
Leeds — 

t.p. Philosophical and Literary Society. Reports, 

p. Yorkshire Geological and Polytechnic Society. Proceedings. 

Liverpool — 

t.p. University College Library. 

p. Biological Society. Proceedings and Transactions, 

p. Geological Society. Proceedings. 

London — 

p. Admiralty. Nautical Almanac and Astronomical Ephemeris. — Health of the 
Navy (Annual Report). 
t.p. Anthropological Institute. Journal. 



345 



1913-14.] List of Library Exchanges, Presentations, etc. 

London — continued — 
t.p. Athenaeum Club. 

British Antarctic Expedition , 1907-09. Reports on Scientific Investigations. 
( Presented . ) 

t.p. British Association for the Advancement of Science. Reports. 
t.p. British Museum ( Copyright Office). Reproductions from Illuminated 

Manuscripts. 

t.p. British Museum. Natural History Department. Catalogues, Monographs, 
Lists, etc. National Antarctic Expedition, 1901-0 If. Publications. 
t.p. Chemical Society. Journal. Abstract of Proceedings, 

p. Faraday Society. Transactions. 

t.p. Geological Society. Quarterly Journal. — Geological Literature. — Abstract of 

Proceedings. 

t.p. Geological Survey of the United Kingdom. Summary of Progress. Memoirs, 

p. Geologists’ Association. Proceedings. 

t.p. Hydrographic Office. 

t.p. Imperial Institute. 

t.p. Institution of Civil Engineers. Minutes of Proceedings, etc. 

t.p. Institution of Electrical Engineers. Journal. 

p. Institution of Mechanical Engineers. Proceedings. 

t.p. International Catalogue of Scientific Literature. [Purchased.) 

t.p. Linnean Society. Journal: Zoology; Botany. — Transactions: Zoology; 

Botany. — Proceedings, 
p. Mathematical Society. Proceedings. 

p. Meteorological Office. Report of the Meteorological Committee to the Lords 
Commissioners of H.M. Treasury. — Reports of the International Meteoro- 
logical Committee. — Hourly Readings. — Weekly Weather Reports. — 
Monthly and Quarterly Summaries. — Meteorological Observations at 
Stations of First and Second Order, and other Publications. Geophysical 
Journal. — Geophysical Memoirs. 

Mineralogical Society of Great Britain and Ireland. Mineralogical Magazine 
and Journal. ( Presented .) 

National Antarctic Expedition, 1901-0 If.. ( Presented .) 

Optical Society. Transactions. ( Purchased .) 
p. Pharmaceutical Society. Journal. — Calendar, 

p. Physical Society. Proceedings. 

t.p. Royal Astronomical Society. Monthly Notices. — Memoirs. 
t.p. Royal College of Surgeons. 

t.p. Royal Geographical Society. Geographical Journal. 

t.p. Royal Horticultural Society. Journal. 

t.p. Royal Institution. Proceedings. 

p. Royal Meteorological Society. Quarterly Journal. 

t.p. Royal Microscopical Society, Journal. 

p. Royal Photographic Society. Photographic Journal. 

t.p. Royal Society. Philosophical Transactions. — Proceedings. — Year-Book. — 
National Antarctic Expedition, 1901-01f, Publications; and other 
Publications. 

Royal Society of Arts. Journal. 



TP. 



346 



Proceedings of the Royal Society of Edinburgh. [Sess. 

London — continued — 
t.p. Royal Society of Literature. Transactions. — Reports. 
t.p. Royal Society of Medicine. Proceedings. 

t.p. Royal Statistical Society. Journal. 

t. p. Society of Antiquaries. Proceedings. — Archseologia ; or Miscellaneous Tracts 
relating to Antiquity. 

Society of Chemical Industry. Journal. ( Presented .) 

Society for Psychical Research. Journal. — Proceedings. (Presented by 

W. C. Crawford , Esq.) 

Solar Physics Committee. Annual Report, and other Publications. 
(Presented.) 

t.p. United Service Institution. 

t.p. University College. Calendar. 

t.p. University. 

t.p. Zoological Society. Transactions. — Proceedings. 

t.p. The Editor of Nature. — Nature. 

t.p. The Editor of The Electrician. — Electrician . 

t.p. The Editor of Science Abstracts. — Science Abstracts. 

Manchester — 

t.p. Literary and Philosophical Society. Memoirs and Proceedings. 
t.p. University . — Publications — Medical Series. Public Health Series. Anatomical 

Series. Physical Series. Biological Series. Lectures. Manchester Museum 
(University of Manchester). Annual Reports — Notes from the Museum, 
p. Microscopical Society. Transactions and Annual Report. 

Ne wcastle-on-Tyne — 

p. Natural History Society of N oi'thumberland , Durham , etc. Transactions. 
t.p. North of England Institute of Milling and Mechanical Engineers. Transac- 
tions. — Annual Reports. 

Cullercoats Dove Marine Laboratory. Annual Report. (Presented.) 
p. Literary and, Philosophical Society. 

University of Durham Philosophical Society. Proceedings. (Presented.) 
p. Norwich. — Norfolk and Norwich Naturalists’ Society. Transactions. 

Oxford — 

t.p. Bodleian Library. 

p. Ashmolean Society. Proceedings and Report. 

p. Raddiffe Observatory. Results of Astronomical and Meteorological Obser- 
vations. 

University Observatory. Astrographic Catalogue. (Presented.) 
p. Penzance. — Royal Geological Society of Cornwall. Transactions. 

t.p, Plymouth. — Marine Biological Association. Journal. 

Richmond (Surrey) — 
t.p. Kew Observatory. 

p. Scarborough. — Philosophical Society. 

t.p. Sheffield. — University College. 

Southport. — Meteorological Observatory. Results of Observations. Joseph 
Baxendell, Meteorologist. (Presented .) . 

t.p. Teddington (Middlesex). — National Physical Laboratory. Collected 
Researches. — Annual Reports. 



347 



1913 - 14 .] List of Library Exchanges, Presentations, etc. 

p. Truro. —Royal Institution of Cornwall. Journal. 

York — 

t.p. Yorkshire Philosophical Society. Reports. 



FINLAND. 

Helsingfors — 

Academics Scientiarum Fennicce. Annales. Sitzungsberichte. — Documenta 
Historica. {Presented.) 

Hydrographisch Biologisch Untersuchungen. { Presented .) 
t.p. Societas Scientiarum Fennica {Societe des Sciences de Finlande). Acta 
Societatis Scientiarum Fennicae. — Ofversigt. — Meteorologisches Jahrbuch. 
— Bidrag till Kannedom om Finlands Natur ocb Folk. 
t.p. Societas pro Fauna et Flora Fennica. Acta. — Meddelanden. 
p. Societe de Geographie de Finlande. Fennia. — Meddelanden. 



FRANCE. 

Besancon. — TJniversite Observatoire National. Bulletin Chronometrique et 
Bulletin Meteorologique. {Presented.) 

Bordeaux— 

t.p. Societe des Sciences Physiques et Natur elles. Memoires. — Observations 

Pluviometriques et Thermometriques. — Proces-Verbaux des Seances, 
p. Societe de Geographie Commerciale. Bulletin. 

Id Observatoire. Catalogue Photographique du Ciel. 
p. Cherbourg. — Societe Nationale des Sciences Naturelles et Mathematiques. 

Memoires. 

p. Concarneau. — College de France {Laboratoire de Zoologie et de Physiologie 

Maritime). Travaux Scientifiques. 
p. Duon. — Academie des Sciences. Memoires. 

Lille — 

t.p. Societe des Sciences. 

t.p. Societe Geologique du Nord. Annales.— Memoires. 

p. TJniversite de France . Travaux et Memoires. 

Lyons — 

t.p. Academie des Sciences, Belles Lettres et Arts. Memoires. 

t.p. Societe d’ Agriculture, Histoire Nat. et Arts. Annales. 

t.p. TJniversite. Annales, Nouv. Serie : — I. Sciences, Medecine. II. Droit, 

Lettres. 

p. Societe Botanique. Annales. — Nouveaux Bulletins, 

p. Societe Linneenne. Annales. 

Marseilles — 

tp. Faculte des Sciences. Annales. 

p. Societe Scientijique Industrielle. Bulletin. 

t.p. Montpellier. — Academie des Sciences et Lettres. Memoires : Section des 
Sciences ; Section des Lettres ; Section de Medecine. Bulletin Mensuel. 



348 



Proceedings of the Royal Society of Edinburgh. [Sess. 

t.p. X antes. — Societe Scientifique des Sciences Naturelles de VOuest de la France. 
Bulletin. 

t.p. Nice. — L’Observatoire. Annales. 

Paris — 

t.p. Academie des Sciences. Comptes Rendus. — Observatoire d’Abbadia : 

Observations, 4to, and other Publications. 
t.p. Academie des Inscriptions et Belles-Lettres. Comptes Bendus. 
t.p. Association Frangaise pour V Avancement des Sciences. Comptes Rendus. 

t.p. Bureau International des Poids et Mesures. — Proces-Yerbaux des Seances, 

— Travaux et Memoires. 
t.p. Bureau des Longitudes. Annuaire. 

p. L’ficole des Pouts et Ghaussees. 

t.p. Ministere de la Marine ( Service Hydrographique.) Annales Hydro- 

graphiques. Expedition de Charcot, 1903-05. (See Presentation List.) 
t.p. Ecole des Mines. Annales des Mines. 

t.p Ecole Normale Superieure. Annales. 

t.p. Fcole Polytechnique. Journal, 

p. Ecole Libre des Sciences Politiques. 

t.p. Institut Oceanographique. Annales. 

t.p. Ministere de V Instruction Publique. Expedition de Charcot, 1908-10. (See 

Presentation List.) 

t.p. Musee Guimet. Revue de l’Histoire des Religions. — Annales. — Bibliotheque 
d’Etudes. 

t.p. Museum d’Histoire Naturelle. Nouvelles Archives. — Bulletin. 
t.p. L' Observatoire. Rapport Annuel sur l’Etat de l’Observatoire. — Annales. — 

Memoires. — Carte Photographique du Ciel. Fol. — Catalogue Plioto- 
graphique du Ciel. 4to. 

L’ Observatoire d’ Astronomie Physique de Meudon. Annales. (Presented.) 
t.p. Societe Nationale d’ Agriculture. Bulletins. — Memoires. 
p. Societe d’ Anthropologie. Bulletin et Memoires. 

t.p. Societe Nationale des Antiquaires. Memoires. — Bulletin. 

t.p. Societe de Biologie. Comptes Rendus. 

t.p. Societe d 1 Encouragement pour V Industrie Nationale. Bulletin. 

t.p. Societe Frangaise de Physique. Journal de Physique.^ — -Annuaire. — Proces- 
Yerbaux. 

t.p. Societe de Geograpliie. La Geographie. 

t.p. Societe Geologique de France. Bulletins. — Memoires (Paleontologie). 

p. Societes des Jeunes Naturalistes et d 1 Etudes Scientifiques. Eeuilles des 

Jeunes Naturalistes. 

t.p. Societe Mathematique. Bulletin. 

p. Societe Philomatliique. Bulletin. 

t.p. Societe Zoologique. Bulletin. — Memoires. 

p. Revue Generate des Sciences Pures et Appliquees. 

t.p. Rennes. — Societe Scientifique et Medicate de VOuest. Bulletin. 

Toulouse^ — 

t.p. TJniversite. — Faculte des Sciences. — U Observatoire. Annales. 

p. Academie des Sciences. Memoires. 



1913-14.] List of Library Exchanges, Presentations, etc. 



349 



GERMANY. 

Berlin — 

Carte Geologigue Internationale de V Europe. Livres I.— VIII. (complete). 

( Presented .) 

t.p. K. Akademie der Wissenschaften. Abhandlungen. — Sitzungsberichte. 
t.p. Physikalische Gesellschaft. Fortschritte der Physik : l te Abtheil ; Physik 
der Materie. 2 te Abtheil ; Physik des Aethers. 3 e Abtheil ; Kosmische 
Physik. — Y erhandlungen. 

t.p. Deutsche Geologische Gesellschaft. Zeitschrift, — Monatsberichte. 

p. Deutsche Meteorologische Gesellschaft. Zeitschrift. 

p. Konigl. Preussisches Meteorologisches Institut. 

p. Gesellschaft Naturforschender Freunde. Sitzungsberichte. — Archiv fair 

Biontologie. 

p. Kgl. Technische Hochschule. Programm. 

t.p. Zoologisches Museum. Mitteilungen. 

Bonn — 

p. Naturhistorischer Verein der Preussischen Rheinlande und Westfalens. Yer- 
handlungen. 

Niederrheinische Gesellschaft fur Natur- und Heilkunde. Sitzungsberichte. 
{Presented.) 

t.p. Bremen. — N aturwissenschaftlicher Verein. Abhandlungen. 
p. Brunswick. — Verein fur Naturwissenschaft. Jahresberichte. 
p. Carlsruhe. — Technische Hochschule. Dissertations, 

p. Cassel. — Verein filr Natur kunde. Berichte. 

t.p. Charlottenburg. — Physikalisch-Technische Reiclisanstalt. Abhandlungen. 
p. Chemnitz. — Naturwissenschaftliche Gesellschaft. Berichte. 
t.p. Dantzic. — Naturforschende Gesellschaft. Schriften. 

I V estpreussischer Botanisch-Zoologischer Verein. Bericht. {Presented.) 
Erlangen — 

t.p. University . Inaugural Dissertations, 

p. Physikalisch-Medicinische Societat. Sitzungsberichte. 

t.p. Frankfurt-am-Main. — Senckenbergische Naturforschende Gesellschaft. Ab- 
handlungen.' — Berichte. 

p. Frankfurt-am-Oder. — N aturwissenschaftlicher Verein. Helios, 

p. Freiburg- i Br. — Naturforschende Gesellschaft. Berichte. 

Giessen — 

t.p. University. Inaugural Dissertations. 

p. Oberhessische Gesellschaft fur Natur- und Heilkunde. Berichte. 

t.p. Gottingen. — K. Gesellschaft der Wissenschaften. Abhandlungen, Neue Folge : 
Math.-Phys. Classe ; Phil.-Hist. Classe. — Nachrichten : Math.-Phys. Cl. ; 
Phil. -Hist. Cl.; Geschaftliche Mittheilungen. — (Gelehrte Anzeigen. 
Purchased.) 

Halle — 

t.p. K. Leopold- Car olinisch- Deutsche Akademie der Naturforscher. Nova Acta 
( Y erhandlungen) . — Leopoldina. 
t.p. Naturforschende Gesellschaft. Abhandlungen. 
p. Verein fur Erdkunde. Mittheilungen. 



350 



Proceedings of the Royal Society of Edinburgh. [Sess. 

Halle — continued — 
p. Naturwissenschaftlicher Verein fur Sachsen und Thuringen. 
p. Deutsche Mathematiker Vereinigung. Jahresbericht. 

Hamburg — 

t.p. Kaiserliche Marine Deutsche Seewarte. Annaleu der Hydrographie, etc. — 
Jahresbericht. 

t.p. Naturwissenschaftlicher Verein. Abhandlungen aus dem Gebiete der Natur- 
ivissenschaften. — Verhandlungen. 

t.p. N aturhistorisches Museum. Jahrbuch. — Beihefte. — Mitteiiungen. 

p. Verein fur Naturwissenschaftliche Unterlialtung. Verhandlungen. 

t.p. Hannover. — Naturhistorische Gesellschaft. Jahresbericht. 
t.p. Helgoland. — K. Biologisches Anstalt. Wissenschaftliche Meeresunter- 
suchungen (Abtheilung Helgoland). 

t.p. Jena. — Medicinisch-Naturwissenschaftliche Gesellschaft. Jenaische Zeitschrift 
fiir Naturwissenschaft. — Denkschriften. 

Kiel — 

t.p. Universitdt. Dissertations. 

t.p. Kommission zur Wissenschaftlichen Untersucliung der Deutschen Meere, 

Wissenschaftliche Meeresuntersuchungen (Abtheilung Kiel), 
p. Naturwissenschaftlicher Verein fur Schleswig-Holstein. Schriften. 

t.p. Konigsberg. — University. 

Leipzig — 

Furstlich Jablonowskisclie Gesellschaft. Preisschriften. ( Presented .) 
t.p. Konigl. Sdchsische Gesellschaft der Wissenschafteu. Berichte : Math.-Phys. 

Classe; Philologisch-Historisclie Classe. — Abhandlungen der Math.-Phys. 
Classe ; Phil. -Hist. Classe. 

t.p. Editor of Annalen der Physik. Annaleu der Physik. 
p. Naturforschende Gesellschaft. Sitzungsberichte. 

Deutsche Mathematiker Vereinigung. ( See Halle.) 
p. Lubeck. — Geographische Gesellschaft und N aturhistorisches Museum. Mitteil- 

ungen. 

p. Magdeburg. — Naturwissenschaftlicher Verein. Abhandlungen u. Berichte. 

t.p. Munich. — K. Bayerische Akademie der Wissenschaften. Abhandlungen: 
Mathematisch-Physikalische Classe ; Philosophisch-Philologische Classe ; 

Historische Classe. — Sitzungsberichte: Mathematisch-Physikalische Classe; 
Philosophiseh-Philol. und Historische Classe.— Jahrbuch. 

K. Sternwarte. Neue Annalen. ( Presented .) 
p. Offenbach. — Verein fiir Naturkunde. Berichte. 

p. Osnabruck. — Naturwissenschaftlicher Verein. Jahresbericht. 

t.p. Potsdam. — Astrophysikalisches Observatorium. Publikationen. 
p. Regensburg. — Historischer Verein von Oberpfalz und, Regensburg. Verhand- 

lungen. 

p. Rostock-i-M. — Naturforschende Gesellschaft. Sitzungsberichte und Abhand- 

lungen. 

p. University. 

t.p. Strassburg. — University. Inaugural Dissertations. 

Bureau Central de V Association International de Sismologie. Publications. 
(. Presented . ) 



351 



1913-14.] List of Library Exchanges, Presentations, etc. 

t.p. Stuttgart. — Verein fur vaterlandische Naturkunde in Wiirttemberg. 
Jahresliefte. 

t.p. Tubingen. — University. Inaugural Dissertations. 



GREECE. 

Athens — 

t.p. University Library. 

t.p. Observatoire National. Annales. 



HAWAIIAN ISLANDS. 

p. Honolulu. — Bernice Pauahi Bishop Museum of Polynesian Ethnology. 

Occasional Papers. — Fauna Hawaiiensis. — Memoirs. 



HOLLAND. 

Amsterdam— 

t.p. Kon. Akademie van Wetenschappen. Verhandelingen : Afd. Natuurkunde. 

l ste Sectie. 2 fce Sectie ; Afd. Letterkunde. — Yerslagen en Mededeelingen ; 
Letterkunde. — Yerslagen der Zittingen van de Wis- en Naturkundige 
Afdeeling. — Jaarboek. — Proceedings of the Section of Sciences. — Poemata 
Latina. 

t.p. Koninklijk Zoologisch Genootschap 11 Natura Artis Magistral Bijdragen 

tot de Dierkunde. 

p. Wiskundig Genootschap. Nieuw Archief voor Wiskunde. — Wiskundige 

Opgaven. — Revue Semestrielle des Publications Mathematiques. 

p. Delft. — itcole Poly technique. Dissertations. 

t.p. Groningen. — University. Jaarboek. 

t.p. Haarlem. — Hollandsche Maatschappij der Wetenschappen. Naturkundige 
Yerhandelingen. —Archives Neerlandaises des Sciences Exactes et 
Naturelles. 

t.p. Musee Teyler. Archives. 

t.p. Helder. — Nederlandsche Dierkundige Vereeniging. Tijdschrift. 

t.p. Leyden. — The University. 

p. Nijmegen. — Nederlandsche Botanische Vereeniging. Nederlandsch Kruidkundig 

Archief. — Yerslagen en Mededeelingen. — Recueil des Travaux Botaniques 
N eerlandaises. 

t.p. Rotterdam. — Bataafsch Genootschap der Proefondervindelijke Wijsbegeerte. 
Nieuwe Yerhandelingen. 

p. Utrecht. — Provinciaal Utrechtsch Genootschap van Kunsten en Weten- 

schappen. Yerslag van de Algemeene Yergaderingen. Aanteekeningen 
van de Sectie Yergaderingen. 8vo. 

Koninklijk Nederlandsch Meteorologiscb Institut. Observations Oceano- 
graphiques et Meteorologiques. — CEuvres Oceanographiques. ( Presented .) 

L' Observatoire. — Recherches Astronomiques. ( Presented .) 



352 



Proceedings of the Royal Society of Edinburgh. [Sess. 



HUNGARY. 

Buda-Pesth— 

t.p. Magyar Tudomanyos Ahademia [. Hungarian Academy). Mathemat. es 
term^szettud. kozlenienyek (Communications Math, and Nat. Sciences). — 
Nyelvtud. kozlemenyek (Philology). — Mathemat. es termeszettud. Ertesito 
(Bulletin, Math, and Nat. Sciences). — Nyelvtudom. Ertekezesek (Philol. 
Memoirs). — Tortenettud. Ertekezesek (Historical Memoirs).— T&rsadalmi 
Ertekezesek (Memoirs, Political Sciences). — Archseologiai Ertesito. — Rap- 
ports. — Almanack. — Mathematische und Naturwissenschaftliche Berichte 
aus Ungarn. — And other publications of the Hungarian Academy, or works 
published under its auspices. 

t.p. Kir-Magy. Termeszettudomanyi Tarsulat ( Royal Hungarian Society of Nat. 
Sciences). 

p. Magyar Kirdlyi Ornithologicii Kozpont [ Royal Hungarian Central-Bureau 
for Ornithology). Aquila. 

ICELAND. 

p. Reikjavik. — Islenzha Fornleifafelag. 

INDIA. 

Bangalore. — Meteorological Results of Observations taken at Bangalore, 
Mysore, Ilassan, and Chitaldroog Observatories ; Report of Rainfall Regis- 
tration in Mysore. ( Presented by the Mysore Government.) 

Bombay — 

t.p. Royal Asiatic Society [ Bombay Branch). Journal. 

t.p. Elphinstone College. 

Archaeological Survey of Western India. Progress Reports. ( Presented .) 

Government Observatory. Magnetic and Meteorological Observations. 
[Presented.) 

Burma. — Reports on Archaeological Work in Burma. ( Presented by the 

Government.) 

Calcutta — 

t.p. Asiatic Society of Bengal. Journal and Proceedings. — Memoirs'. 

Board of Scientific Advice for India. Annual Report. ( Presented .) 

Ethnographical Survey [ Central Indian Agency). Monographs. [Presented.) 

t.p. Geological Survey of India. Records. — Memoirs. — Palaeontologia Indica. 

t.p. Meteorological Office, Government of India. Indian Meteorological Memoirs. 
— Reports. — Monthly Weather Review. 

Archaeological Survey of India. Epigraphia Indica. — Annual Reports. [Pre- 
sented by the Indian Government.) 

Botanical Survey of India. Records. 8vo. [Presented by the Indian 
Government.) 

Imperial Library. Catalogue. [Presented.) 

Linguistic Survey of India. Publications. [Presented by the Indian 

Government.) 



1913-14.] List of Library Exchanges, Presentations, etc. 353 

Calcutta — continued — 

Royal Botanic Garden. Annals. ( Presented .) 
t.p. Indian Museum. Annual Reports. — Records. — Memoirs. — Catalogues, etc. 

Great Trigonometrical Survey. Account of Operations. — Records. — 
Professional Papers. 4to. ( Presented .) 

Fauna of British India, including Ceylon and Burma. 8vo. ( Presented by 
the Indian Government.) 

Indian Research Fund Association. Indian Journal of Medical Research. 
{Presented.) 

Scientific Memoirs, by Medical Officers of the Army of India. 4to. 
( Presented .) 

p. Coimbatore. — Agricultural College and Research Institute. 

Madras — 

t.p. Literary Society. 

Observatory. Report on the Kodaikanal and Madras Observatories. 

8vo. — Bulletins. — Memoirs. ( Presented .) 4to. 

Government Central Museum. Report. ( Presented .) 

A Descriptive Catalogue of the Sanskrit MSS. in the Government Oriental 
Manuscripts Library, Madras. By M. Seshagiri Sastri. 8vo. {Presented 
by the Government of Madras.) 

Rangoon. {See Burma.) 

Simla. Committee for the Study of Malaria. Transactions (Paludism). 
{Presented by the Sanitary Commissioner.) 8vo. 

IRELAND. 

Belfast — 

p. Natural History and Philosophical Society. Proceedings. 

t.p. Queen's University. Calendar. 

Dublin — 

t.p. Royal Irish Academy. Proceedings. — Transactions. — Abstract of Minutes. 
t.p. Royal Dublin Society. Scientific Proceedings. — Economic Proceedings. — 
Scientific Transactions. 
t.p. Library of Trinity College. 

t.p. National Library of Ireland. 

p. Dunsink Observatory. 

Department of Agriculture and Technical Instruction for Ireland — Fisheries 
Branch. Reports on the Sea and Inland Fisheries of Ireland (Scientific 
Investigations). 8vo. — Geological Survey Memoirs. {Presented by the 

Department.) 8vo. 



ITALY. 

Bologna — 

t.p. Accademia di Scienze delV Istituto di Bologna. Memorie. — Rendiconti. 

University Observatory. Osservazioni Meteorologiche. {Presented.) 
t.p. Catania. — Accademia Gioenia di Scienze Naturali. Atti. — Bolletino Mensile. 
t.p. Societa degli Spettroscopisti Italiani. Memorie. 
t.p. Genoa. — Museo Civico di Storia Naturale. Annali. 
p. Messina. — Reale Accademia Peloritana. Atti. 

VOL. xxxiv. 23 



354 Proceedings of the Royal Society of Edinburgh. [Sess. 

Milan- 
as. Osservatorio di Brer a. Publicazioni. ( Presented .) 

t.p. Reale Istituto Lombardo di Scienze , Lettere , ed Arti. Memorie : Classe di 
Scienze Mat. et Nat. ; Classe di Lettere Scienze Storiche e Morali. — 

Rendiconti. 

Modena — 

t.p. Regia Accademia di Scienze, Lettere, ed Arti. Memorie. 
p. Societd dei Naturatisti. Atti. 

t.p. Naples. — Societd Reale di Napoli. Accademia di Scienze Fisiche e Matema- 
tiche. Memorie. — Rendiconti. Accademia di Scienze Morali e Politiche. 
Atti. — Rendiconti. Accademia di Archeologia, Lettere e Belle Arti. 

Atti. — Rendiconti. — Memorie. 
t.p. Stazione Zoologica. Mittheilungen. 

t.p. R. Istituto d.lncoraggiamento. Atti. 

p. Museo Zoologico della R. Universita. Annuario. 

t.p. Padua. — R. Accademia di Scienze, Lettere, ed Arti. Atti e Memorie. 
t.p. Palermo. — Societd di Scienze Naturali ed Economiche. Giornale di Scienze 
Naturali ed Economiche. 

p. Pisa. — Societd Italiana di Fisica. “II Nnovo Cimento.” 

Rome — 

t.p. R. Accademia dei Lincei. Classe di Scienze Fisiche, Math, e Nat. Memorie. 

— Rendiconti. Classe di Scienze Morali, Storiche e Filol. — Notizie degli 

Scavi di Antichita. — Rendiconti. — Memorie. — Annali delh Islam. 
t.p. Accademia Ponteficia dei Nuovi Lincei. Atti. — Memorie. 
t.p. Int. Institute of Agriculture. Monthly Bulletins. 

t.p. R. Comitato G-eologico. Memorie descrittive della Carta Geologica. — 

Bollettino. 

t.p. Societd Italiana di Scienza (detta dei XL.). Memorie. 
p. Sassari. — Istituto Fisiologico della R. Universita di Sassari. Studi Sassaresi. 

Turin — 

t.p. Reale Accademia delle Scienze. Memorie. — Atti. 

Osservatorio della R. Universita. Osservazioni Meteorologiche. 8vo, 
( Presented .) 

t.p. Venice. — R. Istituto Veneto di Scienze, Lettere, ed Arti. Atti. — Osservazioni 
Meteorologiche. 



JAMAICA. 

p. Kingston. — Institute of Jamaica. 

JAPAN. 

p. Formosa. — Bureau of Productive Industry. leones Plantarum Formosanarum. 

p. Sendai. — Tohoku Imperial University. Science Reports. — Tohoku Mathe- 
matical Journal. 

Tokio — 

t.p. Imperial University of Tokio ( Teikoku-Daigaku ). Calendar. — College 
of Science. Journal. — Medicinische Facultdt der Kaiserlich-Japanischen 

Universitat. Mittheilungen. 



355 



1913-14.] List of Library Exchanges, Presentations, etc. 

Tokio— continued — 

p. Zoological Society. Annotationes Zoologicse Japonenses. 

p. Asiatic Society. Transactions, 

p. Deutsche Gesellschaft fur Natur- und Volkerkunde Ostasiens. Mittheilungen. 

p. Imperial Museum. 

Earthquake Investigation Committee. Bulletin. ( Presented .) 
t.p. Kyoto. — Imperial University (College of Science and Engineering). Memoirs. 



JAVA. 

Batavia — 

t.p. Bataviaasch Geriootschap van Kunsten en Wetenschappen. Verhandelingen. — 
Tijdschrift voor Indische Taal-, Land- en Yolkenkunde. — Notulen. 
t.p. Magnetical and Meteorological Observatory. Observations. — Regenwaar- 

nemingen in Nederlandsch-Indie. — Verhandelingen. 
p. Kon. Natuurkundige Vereeniging. Natuurkundig Tijdschrift voor Neder- 
landsch-Indie. 

LUXEMBOURG. 



p. Luxembourg. — Elnstitut Royal Grand-Ducal. Archives trimestrielles. 



MAURITIUS. 

t.p. Royal Alfred Observatory. Annual Reports. — Magnetical and Meteorological 
Observations. 

MEXICO. 

Mexico — 

t.p. Musee National d’Histoire Natur elle. La Xaturaleza, etc. 

t.p. Sociedad Cientifica “ Antonio Alzate.” Memorias. 

t.p. Observatorio Meteorologico-Magnetico Central. Boletin Mensual. 

p. Istituto Geologico. Boletin. Papergones. 

p. Academia Mexicana de Ciencias Exactas, Fisicas y Natur ales. 

p. Tacubaya. — Observatorio Astronomico. Annuario. — Boletin. 



MONACO. 

t.p. Monaco. — Musee Oceanographique. Bulletins. — Resultats des Campagnes 

Scientifiques. 

NATAL. (See UNION OF S. AFRICA.) 

NEW SOUTH WALES. (See AUSTRALIA.) 

NEW ZEALAND. 

Wellington — 

t.p. New Zealand Institute. Transactions and Proceedings. 

New Zealand Government. Statistics of New Zealand. — The New Zealand 
Official Handbook. (Presented by the Government.) 

Colonial Museum and Geological Survey. Publications. (Presented.) 



356 



Proceedings of the Royal Society of Edinburgh. [Sess. 



NORWAY. 

t.p. Bergen. — Museum. Aarsberetning. — Aarbog. — An Account of the Crustacea 
of Norway. By G. 0. Sars. 

Christiania — 

t.p. K. Norske Frederiks Universitet. Nyt Magazin for Naturvidenskaberne. — 
Archiv for Mathematik og Naturvidenskab. 
t.p. Meteorological Institute. Jahrbuch. 

Videnskabs-Selskab. Forhandlinger. — Skrifter (Math. Nat. Kl.). [Presented .) 
p. Stavanger. — Museum. Aarshefte. 

t.p. Throndhjem. — Kgl. Norske Videnskabers Selskab. Skrifter. 
p. Tromso. — Museum. Aarshefter. — Aarsberetning. 

PHILIPPINE ISLANDS. 

p. Manila. — Bureau of Science. Ethnological Survey Publications. Bureau of 

Forestry. Annual Report. 

PORTUGAL. 

t.p. Coimbra. — University. Annuario. Archivo Bibliographico. — Revista. 

Lisbon — 

t.p. Academia das Sciencias de Lisboa. Boletim. — Actas. 
t.p. Sociedade de Geographia. 

Observatorio do Infante D. Luiz. Annaes. ( Presented .) 

Porto. Academia Polytechnica. Annaes Scientificos. 

QUEENSLAND. {See AUSTRALIA.) 

ROUMANIA. 

Bucharest — 

t.p. Academia Romana. Analele. Bulletin de la Section Scientifique. — Also 
Publications relating to the History, etc., of Roumania. Bibliografia 
Romanesca. — Catalogues, etc. 
p. Institut Meteor ologique. Analele. 

RUSSIA. 

t.p. Dorpat (Jurjew). — University. Inaugural Dissertations. — Acta. — Sitzungs- 
berichte der Naturforscher Gesellschaft bei der Universitat. — Schriften. 
t.p. Ekatherinebourg. — Societe Ouralienne d : Amateurs des Sciences Naturelles. 
Bulletin 
Kazan — 

t.p. Imperial University. Uchenuiya Zapiski. 

p. Societe Physico-Mathematique de Kazan. Bulletin. 

t.p. Kiev. — University. Universitetskiya Isvyaistiya. 



1913-14.] List of Library Exchanges, Presentations, etc. 357 

Moscow — 

t.p. Societe Imperiale des Naturalistes . Bulletin. — Nouveaux Memoires. 
t.p. V Observatoire Imperial. Annales. 

t.p. Societe Imperiale des Amis dHistoire Naturelle, d Anthropologie et 
d' Ethnographie. 
t.p. Imperial University. 

t.p. Musee Poly technique. 

p. Observatoire Magnetique et Meteorologique de VUniversite Imperiale. 

p. Odessa. — Societe des Naturalistes de la Nouvelle Russie. Zapiski. 
t.p. Poulkova. — Nicolai Hauptsternwarte. Publications. — Annales. 

St Petersburg — 

t.p. Academie Imperiale des Sciences. Memoires : Classe Phys.-Math. ; Classe 
Hist.-Phil. — Bulletins. 

t.p. Commission Sismique Permanente. Comptes Rendus. — Bulletin. 

t.p. Comite Geologique. Memoires. — Bulletins. — Carte Geologique : Region 

Aurifere d’lenissei : de 1’ Amour : de Lena. 

Commission Royale Russe pour la Mesure dun Arc de Meridien au Spitzberg. 
Missions Scientifiques pour la Mesure d’un Arc de Meridien au Spitzberg 
enterprises en 1899-1902, sous les auspices des Governements Suedois et 
Russe. Mission Russe. 4to. ( Presented .) 
t.p. Imperial University. Scripta Botanica. 

t.p. Institut Imperial de Medecine Experimentale. Archives des Sciences 

Biologiques. 

t.p. Physikalische Central-Observatorium. Annalen. 

t.p. Physico-Chemical Society of the University of St Petersburg. Journal. 

t.p. Russian Ministry of Marine. 

p. Imperial Russian Geographical Society. 

p. K. Miner alogische Gesellschaft. Verhandlungen (Zapiski). — Materialien zur 
Geologie Russlands. 

p. Societe des Naturalistes ( Section de Geologie et de Miner alogie). Travaux et 
Supplements. 

p. Societe Astronomique Russe. 

p. Tiflis. — Physikalisches Observatorium. Beobachtungen. 



SCOTLAND. 

t.p. Aberdeen. — University Library. Calendar. — University Studies. — Library 





Bulletin. 




p. 


Berwickshire. — Naturalists ’ Club. Proceedings. 




T.P. 


Dundee. — University College Library. 
Edinburgh — 




T.P. 


Advocated Library. 




P. 


Botanical Society. Transactions and Proceedings. 
Carnegie Trust for the Universities of Scotland. 


Report. ( Presented .) 


P. 


Faculty of Actuaries in Scotland. Transactions. 




P. 


Fishery Board for Scotland. Annual Reports. 


Scientific Investigations. — 



Salmon Fisheries. Fifth Report of the Fishery and Hydrographical Investi- 
gations in the N. Sea and Adjacent Waters (1908—1911). Fol. Lond. 1913. 



358 



p. 

T.P. 

P. 

P. 

T.P. 

T.P. 

P. 

T.P. 

T.P. 

T.P. 

P. 

T.P. 

P. 

T.P. 

P. 

T.P. 

P. 

P. 

T.P. 

T.P. 

P. 

P. 

T.P. 

T.P. 



T.P. 

T.P. 

P. 



P. 

T.P. 



Proceedings of the Royal Society of Edinburgh. [Sess. 

Edinburgh — continued — 

Geological Society. Transactions. 

Geological Survey of Scotland. Memoirs, Maps, etc. ( Presented by H.M. 
Government.) 

Highland and Agricultural Society of Scotland. Transactions. 

Mathematical Society. Proceedings. — Mathematical Notes. 

Pharmaceutical Society. ( North British Branch). 

Registrar-General’ s Returns of Births, Deaths, and Marriages. (Presented.) 
Royal Botanic Garden. Notes. 

Royal College of Physicians. 

Royal College of Physicians’ Laboratory. Laboratory Reports. 

Royal Medical Society. 

Royal Observatory. Annals. — Annual Report. 

Royal Physical Society. Proceedings. 

Royal Scottish Academy. Annual Reports. (Presented.) 

Royal Scottish Geographical Society. Scottish Geographical Magazine. 

Royal Scottish Society of Arts. Transactions. 

Scottish Meteorological Society. Journal. 

Scottish National Antarctic Expedition. Publications. (Presented.) 
University Library. Calendar. 

Glasgow — 

Geological Society. Transactions. 

Royal Technical College. Calendar. (Presented.) 

Inst, of Engineers and Shipbuilders in Scotland. Transactions. 

Marine Biological Association of the West of Scotland. Annual Report. 
See Millport. 

Natural History Society . — Glasgow Naturalist. 

Royal Philosophical Society. Proceedings. 

University. Calendar. 

University Observatory. 

Millport. — Marine Biological Association of the West of Scotland . Annual 
Report. 

Perth. — Perthshire Society of Natural Science. Proceedings. 

St Andrews. — University Library. Calendar. 



SPAIN. 

Madrid — 

Real Academia de Ciencias Exactas , Fisicas y Naturales. Memorias. — 
Re vista. — Annuario. 

Instituto Geologico de Espaha. Boletin. — Memorias. 

Vilafranca del Panades (Cataluna). — Observatorio Meteorologico. 



SWEDEN. 

Gothenburg. — Kongl. Vetenskaps och Vitterhets Samhdlle. Handlingar. 

Lund. — University. Acta TJniversitatis Lundensis (Fysiografiska Sallskapets 
Handlingar. — Theologi. — Medicina). 



1913-14.] List of Library Exchanges, Presentations, etc. 359 

t.p. Stockholm. — Kong. Svenska Vetenskaps-Akademie. Handlingar. — Arkiv for 
Zoologi. — Arkiv for Matematik, Astronomi och Fysik. — Arkiv for 
Botanik. — Arkiv for Kemi, Mineralogi och Geologi. — Meteorologiska 
Iakttagelser i Sverige. — Astronomiska Iakttagelser. — Lefnadsteckningar. — 
Arsbok. — Accessionskatalog. — Meddelanden fr&n K.Vetenskaps Akademiens 
Nobelinstitut. — Les Prix Nobel. 

p. Svenska Sallskapet for Antropologi och Geograji. Ymer. 

Commission Roy ale Suedoise pour la Mesure Pun Arc de Meridien au 
Spitzberg. Missions Scientifiqnes pour la Mesure d’un Arc de Meridien 
au Spitzberg entreprises en 1899-1902, sous les auspices des Gouverne- 
ments Suedois et Russe. Mission Suedoise. 4 to. ( Presented .) 

Ups ala— 

t.p. Kongliga Vetenskaps Societeten {Regia Societas Scientiarum). Nova Acta. 

t.p. University. Arsskrift. — Inaugural Dissertations (Medical and Scientific). — 
Bulletin of the Geological Institution. 

Observatoire de V Universite. Bulletin Meteorologique Mensuel. 



SWITZERLAND. 

t.p. Basle. — Naturforschende Gesellschaft. Verhandlungen. 

Bern — 

Commission Geodesique Suisse. Arbeiten. {Presented.) 
t.p. Societe Helvetique des Sciences Naturelles. {Allgemeine Schweizerische 

Gesellschaft fiir die gesammten Naturwissenschaften.) Comptes Rendus. — 
Actes (Verhandlungen). — Nouveaux Memoires. 
p. Naturforschende Gesellschaft. Mittheilungen. 

t.p. Geneva. — Societe de Physique et PHistoire Naturelle. Memoires. — Comptes 
Rendus. 

p. Lausanne. — Societe Vaudoise des Sciences Naturelles. Bulletin. — Observations 

Meteorologiques. 

Neuchatel — 

t.p. Societe des Sciences Naturelles. Bulletin, 

p. Societe Neuchateloise de Geographic. Bulletin. 

Zurich — 
t.p. University. 

t.p. Commission Geologique Suisse. Beitrage zur geologischen Karte der 

Schweiz. 

t.p. Naturforschende Gesellschaft. Vierteljahrsschrift. 
p. Schioeizerisclie Botanische Gesellschaft. Berichte (Bulletin). 

Schweizerische Meteor ologische Central- Anstalt. Annalen. 4 to. {Presented.) 



TASMANIA. {See AUSTRALIA.) 



TRANSVAAL. {See UNION OF S. AFRICA.) 



360 Proceedings of the Royal Society of Edinburgh. [Sess. 



TURKEY. 



p. Constantinople. — Societe Imperiale de Medecine. Gazette Medicate d’Orient. 



UNION OF SOUTH AFRICA. 

Cape Town — 

p. Royal Society of South Africa. Transactions. 

t.p. Royal Astronomical Observatory. Reports. — Annals. — Meridian Observations. 
— Independent Day Numbers. 

p. Geological Commission (now Survey). Annual Reports. 
t.p. South African Museum. Annals. 

p. South African Association for the Advancement of Science. Journal. 

J OHANNESBURG 

t.p. Geological Society of South Africa. Transactions and Proceedings. 
t.p. Union Observatory. Circulars. 

Pietermaritzburg — 

p. Geological Survey of Natal. Annual Reports. — Reports on the Mining 
Industry of Natal. 

t.p. Government Museum. Annals. — Catalogues. 

Pretoria — 

Dept, of Mines — Geological Survey. Reports. — Memoirs. — Maps. [Presented.) 
t.p. Transvaal Museum. Annals. 



UNITED STATES OF AMERICA. 

Albany — 

t.p. New York State Library. Annual Reports. — Bulletins. 

State Museum. Annual Reports. — Bulletin. Neiv York State Education 
Department. Annual Reports, 
p. Allegheny. — Observatory. Publications, etc. 

p. Ann Arbor. — Michigan Academy of Sciences. Reports. ( University .) 
p. Annapolis (Maryland). — St John’s College. 
p. Austin. — Texas Academy of Sciences. Transactions. 

t.p. Baltimore. — Johns Hopkins University. American Journal of Mathematics. — 
American Chemical Journal. — American Journal of Philology. — University 
Studies in Historical and Political Science. — Memoirs from the Biological 
Laboratory. — U ni versity Circulars . 

Johns Hopkins Hospital. Bulletins. — Reports. ( Presented .) 
t.p. Maryland Geological Survey. Publications. 

Maryland Weather Service. Reports. [Presented.) 

Peabody Institute. Annual Reports. [Presented.) 

Berkeley (California) — 

t.p. University of California. — University Chronicle. — Reports of Agricultural 
College. — Publications (Zoology, Botany, Geology, Physiology, Pathology 
and American Archaeology and Ethnology). — Memoirs. 

Academy of Pacific Coast History. Publications. 



361 



1913-14.] List of Library Exchanges, Presentations, etc. 

Boston — 

t.p. Bowditch Library. 
t.p. Boston Society of Natural History. Memoirs. — Proceedings. — Occasional 
Papers. 

t.p. American Academy of Arts and Sciences. Memoirs. — Proceedings, 
p. Brooklyn. — Institute of Arts and Sciences. Museum Reports. — Bulletins, 

p. Buffalo. — Society of Natural Sciences. Bulletin. 

California. ( See San Francisco, Sacramento, Berkeley, Mount Hamilton, 
Mount Wilson and Stanford.) 

Cambridge — 

t.p. Harvard University. — Museum of Comparative Zoology. Memoirs. — 
Bulletins — Annual Reports. 

t.p. Astronomical Observatory , Harvard College. Annals. — Annual Reports. — 
Observatory Circulars. 

p. Chapel Hill (North Carolina). — E. Mitchell Scientific Society. Journal, 
p. Charlottesville. Philosophical Society , University of Virginia. Bulletin ; 

Scientific Series and Humanistic Series. — Proceedings. 

Chicago — 

t.p. Field Museum of Natural History. Publications : Geological Series ; 

Botanical Series ; Zoological Series ; Ornithological Series ; Anthropo- 
logical Series. — Annual Reports, 
p. University of Chicago. 

t.p. Yerkes Observatory ( University of Chicago). Publications, 
p. Academy of Sciences. Bulletins. — Special Publications.— Bulletins of the 
Natural History Survey. 

Cincinnati — 

p. Observatory (University). Publications. — University Record, 

p. Society of Natural History. Journal. 

t.p. Cleveland (Ohio). — Geological Society of America. Bulletins. 
t.p. Clinton (Iowa). — Litchfield Observatory , Hamilton College. 

Colorado Springs. — Colorado College. Colorado College Studies. (Pre- 
sented.) 

p. Connecticut. — Connecticut Academy of Arts and Sciences. Transactions. 
— Memoirs. 

p. Davenport. — Academy of Natural Sciences. Proceedings, 

p. Denver (Colorado). — Scientific Society of Colorado. Proceedings. 
t.p. Des Moines (Iowa). — Iowa Academy of Sciences. Proceedings, 
p. Garrison, N.Y. — Editor, American Naturalist. 

t.p. Granville (Ohio). — Denison University and Scientific Association. Bulletin of 
the Scientific Laboratories. 

p. Indianopolis. — Indiana Academy of Sciences. Proceedings. 

Iowa City — 

p. Geological Survey. Annual Reports. 

p. State University. Laboratories of Natural History. Bulletins. — Contribu- 
tions from the Physical Laboratories. 

Iowa. ( See Des Moines.) 

Ithaca (N.Y.) — 

p. The Editor, Physical Review. (Cornell University.) 



362 



Proceedings of the Royal Society of Edinburgh. [Sess. 



Ithaca (N.Y.) — continued — 

p. The Editors, Journal of Physical Chemistry. (Cornell University.) 
t.p. Lawrence (Kansas ). — University of Kansas. Science Bulletin (University 
Quarterly). 

p. Lincoln (Nebraska). — University of Nebraska. Agricultural Experiment 
Station. Bulletins. 

Madison — 

t.p. Wisconsin University. Washburn Observatory. Observations, 

p. Wisconsin Academy of Sciences , Arts , and Letters. Transactions, 
p. Geological and Natural History Survey. Bulletins, 

p. Massachusetts . — Tufts College Library. Tufts College Studies, 

p. Meriden (Conn .). — Meriden Scientific Association. 

Michigan. ( See Ann Arbor.) 

Minneapolis (Minn.) — 

T I University of Minnesota. Studies. — Bulletin of the School of Mines. 

( Geological and Natural History Survey of Minnesota. Reports, 
p. Botanical Survey. 

Missouri. (See St. Louis and Rolla.) 

p. Mount Hamilton (California ). — Lick Observatory. Bulletins. — Publica- 

tions. 

t.p. Mount Wilson (California ). — Solar Observatory . Contributions. — Reports. 
t.p. Newhaven (Conn .) — Yale College. Astronomical Observatory of Yale University. 

Transactions. — Reports, 
p. New Orleans . — Academy of Sciences. 

New York — 

t.p. American Mathematical Society. Bulletins. — Transactions. 

t.p. American Museum of Natural History. Bulletins. — Memoirs. — American 

Museum Journal. — Annual Reports. — Anthropological Papers. — Guide 
Leaflets. — Handbook Series. — Monograph Series, 
p. American Geographical Society. Bulletin, 

p. American Institute of Electrical Engineers. Proceedings. 

New York. (See also Albany.) 

Philadelphia — 

t.p. American Philosophical Society for Promoting Useful Knowledge. Proceedings. 

— Transactions. 

t.p. Academy of Natural Sciences. Proceedings. — Journal. 

t.p. University of Pennsylvania. Publications : — Philology, Literature, and 

Archaeology, Mathematics, etc. Contributions from the Zoological and 
Botanical Laboratories. University Bulletins.— Theses. — Calendar. 
t.p. Geological Survey of Pennsylvania. 

p. Wagner Free Institute of Science. Transactions, 

p. Geographical Society. Bulletin, 

p. Commercial Museum. 

p. Portland (Maine ). — Society of Natural History. Proceedings, 
p. Princeton, N.J. — University. Annals of Mathematics. — University Obser- 
vatory. Contributions. 

p. Rochester . — Academy of Science. Proceedings. 

t.p. Rolla (Miss .).-— Bureau of Geology and, Mines. Biennial Reports, etc. 



1913-14.] List of Library Exchanges, Presentations, etc. 363 

t.p. [Salem. — Essex Institute. 

Saint Louis — 

t.p. Academy of Sciences. Transactions, 

p. Missouri Botanical Garden. Annual Reports, 

p. Washington University. University Studies. 

t.p. San Francisco (California). — Academy of Sciences. Proceedings. — Memoirs. 
— Occasional Papers. 

Stanford (California). — University. Publications. ( Presented .) 
p. Topeka. — Kansas Academy of Science. Transactions. 

t.p, Urbana. — University of Illinois. Bulletins of State Geological Survey , State 
Laboratory of Natural History , and Engineering Experiment Station . 

Washington — 

t.p. U.S. National Academy of Sciences. Memoirs. 
t.p. Bureau of Ethnology . Annual Reports. — Bulletins. 
t.p. U.S. Coast and Geodetic Survey. Annual Reports, etc. 
t.p. U.S. Commission of Fish and Fisheries. Reports. — Bulletins. 
t.p. U.S. Naval Observatory. Reports. — Observations. 

t.p. U.S. Geological Survey. Bulletins. — Annual Reports. — Monographs. — 

Geologic Atlas of the United States. — Mineral Resources. — Professional 
Papers. — Water Supply and Irrigation Papers. 

Geological Society of America. ( See Cleveland.) 
t.p. Weather Bureau. (Department of Agriculture.) Monthly Weather Review. 

— Bulletins. — Reports. — Bulletin of the Mount Weather Observa- 
tory (now embodied in Monthly Weather Review). 
t.p. Smithsonian Bistitution. Miscellaneous Collections. — The same (Quarterly 
Issue). — Contributions to Knowledge.- — Reports. — Annals of the Astro- 
physical Observatory. — Harriman Alaska Expedition, Yol. XIV. 4to. 
t.p. Surgeon-General’s Office. Index Catalogue of the Library. 4to. 
t.p. Carnegie Institution of Washington. Year-Books. — Publications. Classics 

of International Law. — Carnegie Foundation for the Advancement of 
Teaching. Annual Report. — Bulletin. 
t.p. American Association for the Advancement of Science. Proceedings, 
p. U.S. National Museum. Bulletins. — Reports. — Proceedings. — Contributions 
from the U.S. National Herbarium. 

p. Department of Agriculture. ( Division of Economic Ornithology and 
Mammalogy.) Bulletin, 
p. U.S. Patent Office. 

Washington Academy of Sciences , Journal of the. (Purchase.) 

Bureau of Standards. Department of Commerce and Labour. Bulletins. 
(Presented. ) — Technologic Papers. 

Wisconsin. (See Madison.) 



VICTORIA. (See AUSTRALIA.) 



364 



Proceedings of the Royal Society of Edinburgh. [Sess. 



List of Periodicals and Annual Publications added to the 
Library by Purchase, etc. 

Periodicals not found in this List will be found in Exchange List. 

Annuals ( Works of Reference ), see end of List. 

Acta Mathematica. 

American Journal of Science and Arts. 

* Naturalist. 

* Journal of Mathematics. 

* Chemical Journal. 

* Journal of Philology. 

Anatomischer Anzeiger. 

Erganzungshefte. 

Annalen der Chemie (Liebig’s). 

* der Physik. 

* der Physik. (Beiblatter.) 

Annales de Chimie. 

d’Hygiene Publique et de Medecine Legale. 

de Physique. 

des Sciences Naturelles. Zoologie et Paleontologie. 

des Sciences Naturelles. Botanique. 

Annali dell’ Islam. (Presented.) 

Annals and Magazine of Natural History (Zoology, Botany, and Geology). 

of Botany. 

* of Mathematics. (Princeton, N.J.) 

Anthropologie (L’). 

Arbeiten-Zoologisches Institut der Universitat und der Zoologischen Station in Triest. 

* Archiv for Mathematik og Naturvidenskab. 

* Archiv fur Biontologie. 

Archives de Biologie. 

de Zoologie Experimental et Generale. 

* des Sciences Biologiques. 

des Sciences Physiques et Naturelles. 

Italiennes de Biologie. 

* Arkiv for Matematik, Astronomi och Fysik. (Stockholm.) 

* for Kemi, Mineralogi och Geologi. ,, 

* — - — for Botanik. „ 

* for Zoologi. ,, 

Astronomie (L’). 

Astronomische Nachrichten. 

Astrophysical Journal. 

Athenaeum. 

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1914. ( Presented by the A uthor. ) 



369 



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Co. Ltd.) Fol. Rangoon, 1909. (Presented by the Author.) 

Stuckney, (J. J.). Table of Compound Interest at 1/8 per cent, and of Anti- 
logarithms to Base 1 ‘00125. 4to. London, 1914. (Presented by the Author.) 
Uppsala, Zoologiska Bidrag fran (med understbd af R. Biinsows Zoologiska Fond.). 

Utgifna af A. Wiren. Bd. 1, 2. 8vo. Uppsala, 1911-13. (Presented.) 
Yersluys (J.). Contribution a la Theorie de l’Ecoulement de l’Eau Souterraine. 

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VOL. XXXIV. 



24 



INDEX. 



Abnormalities in Echinoids, by James Ritchie 
and James A. Todd, 241-252. 

Additions to Library, 368. 

Address, Opening, from James Geikie, President, 
4-9. 

Analytical Study of the Mechanism of Writing, 
by James Drever, 230-240. 

Anderson (E. M.). The Path of a Ray of Light 
in a Rotating Homogenous and Isotropic 
Solid. See also Larmor., Sir Joseph, 69-76. 

Antarctica, Notes on the Evolution of, by 
T. W. Edgeworth David ( Title only), 296. 

Atmosphere, Circulation of the, by W. N. Shaw., 
77-112. 

Atmospheric Electrical Potential Gradient in 
Industrial Districts, by Steuart and Jorgensen, 
202-207. 

Motion, Laws of, by W. N. Shaw, 79. 

Persistence of, by W. N. Shaw, 88. 

Structure, Computation from Soundings 

with a Pilot Balloon, by W. N. Shaw, 97. 

Auditory Organ in the Cetacea, by Sir Wm. 
Turner, 10-22. 

Australian Aboriginal. His relation to the 
Tasmanian Aboriginal as deduced from a 
S'tudy of the Calvaria. Part II. , by R. J. A. 
Berry and A. W. D. Robertson, 144-189. 

Berry (R. J. A.) and A. W. D. Robertson. The 
place in Nature of the Tasmanian Aboriginal 
as deduced from a Study of his Calvaria. 
Part II. — His relation to the Australian 
Aboriginal, 144-189. 

Bigradients, Theory of, from 1859-1880, by 
Thomas Muir, 32-59. 

Buchner (L. W. G. ). A Study of the Curva- 
tures of the Tasmanian Aboriginal Cranium, 
128-143. 

Bust of Lord Kelvin, Presentation of ( Frontis- 
piece ), 1-3. 

Cetacea, Auditory Organ in, by Sir Wm. 
Turner, 10-22. 

Circulation of the Atmosphere, Study of, by 
W. N. Shaw, 77-112. 

Clague (T. M.). See Oliver, Sir Thomas. 

Continuants, Some Factorable, by W. H. 
Metzler, 223-229. 

Convection of Air in the General Circulation of 
the Atmosphere, by W. N. Shaw, 81, 107. 

Court (Dorothy). Enzymatic Peptolysis in 
Germinating Seeds, 113-127. 

Cranium, Curvatures of the Tasmanian Abo- 
riginal, by L. W. G. Buchner, 128-143. 

Curvatures of the Tasmanian Aboriginal 
Cranium, by L. W. G. Buchner, 128-143. 



Darbishire (A. D.) and M. W. Gray. On the 
Inheritance of Certain Characters of the Wool 
of Sheep {Title only), 297. 

David (T. W. Edgeworth). Notes on the 
Evolution of Antarctica {Title only), 296. 

Determinant, Some Factorable Minors of a 
Compound, by W. H. Metzler, 27-31. 

Drever (James). The Analytical Study of the 
Mechanism of Writing, 230-240. 

Echinoids, Abnormal, in the Collection of the 
Royal Scottish Museum, James Ritchie and 
James A. Todd, 241-252. 

Enzymatic Peptolysis in Germinating Seeds, by 
Dorothy Court, 113-127. 

Exchanges, Library, List of, 340. 

Fellows, Honorary, at January 1, 1915, 337-338. 

Ordinary, Elected during Session 1913— 

1914, 339. 

List of Ordinary at January 1, 1915, 

320-337. 

Deceased and Resigned during Session 

1913-1914, 339. 

Four- dimensional Figure, Projection-Model of, 
by D. M. Y. Sommerville, 253-258. 

Geikie (Janies). Opening Address, 4-9. 

Gibson (A. H. ). The Kinetic Energy of Viscous 
Flow through a Circular Tube, 60-63. 

Gibson (John), Obituary Notice of, 285-288. 

Gray (M. W. ). See Darbishire, A. D. 

Gunther (A. C. L. G. ), Obituary Notice of, 
269-277. 

Gunning Victoria Jubilee Prize, Regulations, 
etc., for Award of, 305-311. 

Hall, and Transverse Thermomagnetic Effects 
and their Temperature Coefficients, by F. 
Unwin, 208-222. 

Eexadinellida, Siliceous Sponge of the Order, 
from S. Shetland, by Sir Wm. Turner, 23-26. 

Inheritance of Certain Characters of the Wool 
of Sheep, by A. D. Darbishire and M. W. 
Gray {Title only), 297. 

Ionisation by Combustion, and Atmospheric Elec- 
tricity, by Steuart and Jorgensen, 202-207. 

Jorgensen (Invar). See Steuart, Dan. W. 

Keith Prize, Award of, to James Russell, period 
1911-1913, 298. 

Regulations, etc., for Award, 

305-311. 

Kelvin (Lord), Presentation of Bust of {Frontis- 
piece), 1-3. 



370 



Index. 



371 



Kinetic Energy of Viscous Flow through a 
Circular Tube, by A. H. Gibson, 60-63. 

Knott (C. G.). Changes of Electrical Resist- 
ance accompanying Longitudinal and Trans- 
verse Magnetizations in Iron and Steel, 259- 
268. 

Larmor (Sir Joseph). Note on Mr Anderson’s 
Paper, ‘ ‘ Path of a Ray of Light in a Rotating 
Solid,” 69-76. 

Laurie (A. P. ). Obituary Notice of John 
Gibson, 285-288. 

Lead-poisoning, Electrolytic Treatment of. See 
Thomas Oliver and T. M. Claque ( Title only), 
296. 

Library, Additions to, 368. 

Library Exchanges, List of, 340. 

Light, Path of a Ray of, in a Rotating Solid, 
by E. M. Anderson, 69-76. 

Mackay (John Sturgeon), Obituary Notice of, 
278-284. 

MTntosh (W. C.). Obituary Notice of 

A. C. L. G. Gunther, 269-277. 

M'Whan (J.). The Axial Inclination of Curves 
of Thermoelectric Force : a Case from the 
Thermoelectrics of Strained Wires, 64-68. 

Magnetization, Longitudinal and Transverse, 
Effect on Resistance of Iron, by C. G. Knott, 
259-268. 

Makdougall-Brisbane Prize, Regulations, etc., 
for Award of, 305-311. 

Metzler (W. H.). Some Factorable Con- 
tinuants, 223-229. 

Some Factorable Minors of a Compound 

Determinant, 27-31. 

Minors of a Compound Determinant, 

Some Factorable, 27-31. 

Model of the 600-Cell in Space of Four Dimen- 
sions, by D. M. Y. Sommerville, 253- 
258. 

Muir (Thomas). The Theory of Bigradients 
from 1859-1880, 32-59. 

Museum, Royal Scottish, Abnormal Echinoids 
in the Collection of, by Janies Ritchie and 
James A. Todd, 241-252. 

Neill Prize, Award of, to W. S. Bruce, period 

1911- 13, 298. 

Regulations, etc., for Award, 305-311. 

Obituary Notices of Fellows deceased in Session 

1912- 1913. See President’s Opening Address, 
4-9. 

A. C. L. G. Gunther, 269-277 ; 

John Sturgeon Mackay, 278-284 ; John 
Gibson, 285-288. 

Oliver (Sir Thomas) and T. M. Claque. The 
Electrolytic Treatment of Lead-poisoning 
( Title only), 296. 

Oil-shales, Organic Matter in, by John B. 
Robertson, 190-201. 

Peptolysis, Enzymatic, in Germinating Seeds, 
by Dorothy Court, 113-127. 

Periodicals, etc., List of, 364. 

Philip (George). Obituary Notice of J. S. 
Mackay, 278-284. 



Poisoning, Electrolytic Treatment of Lead-, by 
Sir Thomas Oliver and T. M. Claque ( Title 
only), 296. 

President’s Opening Address, 4-9. 

Prizes. See Keith, Makdougall-Brisbane, Neill, 
and Gunning Victoria Jubilee Prizes, 305-11. 

Resistance of Iron in Crossed Magnetic Fields, 
Change of, by C. G. Knott, 259-268. 

Ritchie (James) and James A. Todd. Abnormal 
Echinoids in the Collection of the Royal 
Scottish Museum, 241-252. 

Robertson (A. W. D.). See Berry, R. J. A. 

Robertson ( J ohn B. ). A Chemical Examination 
of the Organic Matter in Oil- Shales, 190-201. 

Rotating Solid, Path of a Ray of Light in, by 
E. M. Anderson, 69-76. 

Seeds, Enzymatic Peptolysis in, by Dorothy 
Court, 113-127. 

Shaw (W. N.). Principia Atmosph erica, a 
Study of the Circulation of the Atmosphere, 
77-112. 

Sheep, Inheritance of Certain Characters of the 
Wool of, by A. D. Darbishire and M. W. 
Gray ( Title only), 297. 

Siliceous Sponge of the Order Hexactinellida 
from South Shetland, by Sir Wm. Turner, 
23-26. 

Smoke, and Atmospheric Electricity, by Steuart 
and Jorgensen, 202-207. 

Sommerville (D. L. Y.). Description of a 
Projection-model of the 600-Cell in Space of 
Four Dimensions, 253-258. 

Sponge, Siliceous, of the Order Hexactinellida 
from South Shetland, by Sir Wm. Turner, 
23-26. 

Steuart (Dan. W. ) and Ingvar Jorgensen. 
N otes on the Atmospheric Electrical Potential 
Gradient in the Industrial Districts around 
Leeds, 202-207. 

Tasmanian Aboriginal Cranium, A Study of the 
Curvatures of, by L. W. G. Buchner, 128-143. 

Tasmanian Aboriginal, His Relation to the 
Australian Aboriginal as deduced from a 
Study of his Calvaria. Part II. By R. J. A. 
Berry and A. W. D. Robertson, 144-189. 

Thermomagnetic Effects, Transverse, and Hall 
Effect, Temperature Coefficients of, by F. 
Unwin, 208-222. 

Thermoelectric Force, Axial Inclination of 
Curves of, by J. M‘Whan, 64-68. 

Todd (James A.). See Ritchie, James. 

Turner, Sir Wm. Note on a Siliceous Sponge 
of the Order Hexactinellida from South Shet- 
land, 23-26. 

Observations on the Auditory Organ in 

the Cetacea, 10-22. 

Unwin, F. On the Hall and the Transverse 
Thermomagnetic Effects and their Tempera- 
ture Coefficients, 208-222. 

Viscous Flow, The Kinetic Energy of, by A. H. 
Gibson, 60-63. 

Writing, The Analytical Study of the Mechanism 
of, by James Drever, 230-240. 



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MODEL INDEX. 

Schafer, E. A. — On the Existence within the Liver Cells of Channels which can be directly 
injected from the Blood-vessels. Proc. Roy. Soc. Edin. , vol. , 1902, pp. 

Cells, Liver, — Intra-cellular Canaliculi in. 

E. A. Schafer. Proc. Roy. Soc. Edin., vol. 

Liver, — Injection within Cells of. 

E. A. Schafer. Proc. Roy, Soc. Edin., vol. 



, 1902, pp. 
, 1902, pp 



IV 



CONTENTS. 




PAGE 

Obituary Notices — 

Dr A. C. L. G. Gunther, M.A., Ph.D., M.D., LL.D., F.R.S., etc. 

By William C. MTntosh, . . . . .269 

John Sturgeon Mackay, M.A., LL.D. By George Philip, 

M.A., D.Sc., . . . . . 278 

Professor John Gibson. By Principal A. P. Laurie, D.Sc., . 285 

Appendix — 

Laws of the Society, . . . . . . 293 

The Keith, Makdougall-Brisbane, Neill, and Gunning Victoria 

Jubilee Prizes, . . . . . . 298 

Awards of the Keith, Makdougal] -Brisbane, Neill, and Gunning 

Victoria Jubilee Prizes, ..... 300 

Proceedings of the Statutory General Meeting, October 1913, . 305 

Proceedings of the Ordinary Meetings, Session 1913-1914, . 306 

Proceedings of the Statutory General Meeting, October 1914, . 312 

Accounts of the Society, Session 1913-1914, . . . 313 

The Council of the Society at October 1914, . . . 319 

Alphabetical List of the Ordinary Fellows of the Society at 

January 1915, ...... 320 

List of Honorary Fellows of the Society, January 1915, . 337 

List of Ordinary Fellows of the Society elected during Session 

1913-1914, ....... 339 

Honorary Fellows and Ordinary Fellows Deceased and Resigned 

during Session 1913-1914, ..... 339 

List of Library Exchanges, ..... 3A) 

List of Periodicals Purchased by the Society, . . .364 

Additions to Library during 1914, by Gift or Purchase, . . 368 

Index, ......... 370 



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